1
vote
1answer
30 views

Solving $Ax=B$: what's wrong with this linear algebra argument?

With $K>L$ and assuming that we are working with real variables, suppose that $B$ is $K\times 1$ and $A$ is $K\times L$ with full column rank. I'm trying to find $x$ ($L\times 1$) satisfying: $$ ...
0
votes
1answer
35 views

Find the standard matrix of the linear transformation

Suppose there is a linear transformation $T:\mathbb{R^2} \rightarrow \mathbb{R^2}$ such that $$T\left( \begin{array}{ccc}2 \\ 1 \end{array} \right)=\left( \begin{array}{ccc}1\\ 4 \end{array} ...
0
votes
1answer
25 views

Mixture problem might be missing something

A winemaker wants to mix a $10\%$ alcohol wine with $20 \text{ kg}$ of a $55\%$ wine to make a $35\%$ wine cooler. How much of the $10\%$ should be used? I started with $.1x+.55y=.35$ then I'm not ...
1
vote
2answers
41 views

Evaluate a linear system of three equations

Solve for $x, y\ \text{and}\ z\ $: $x-3z=10\\ -x+y+2z=7\\ 2x+2y-5z=-8$ My working: $$\left(\begin{array}{ccc|c} 1 & 0 & -3 & 10 \\ -1 & 1 & 2 & 7 \\ 2 & 2 & -5 & ...
1
vote
1answer
54 views

Rational solution to AX=0

Let $\mathcal{M}_{n,p}(\mathbb{K})$ be the set of matrices $n\times p$ with coefficients in $\mathbb{K}$. Let $A\in\mathcal{M}_{n,p}(\mathbb{Q})$. We suppose there exists a non zero solution ...
0
votes
1answer
15 views

Creating a system of linear equations.

An average mark is computed for 100 students in Business, an average is computed for 300 students in Arts, and an average is computed for 200 students in Science. The average of these three averages ...
0
votes
3answers
34 views

Creating a system of linear equations

A bookkeeper is trying to determine the prices that a manufacturer was charging by examining old sales slips, which show the number of various items shipped and the total price. He finds that $20$ ...
2
votes
1answer
42 views

Solving systems of linear equations.

I'm just curious at to creating the system of linear equations for the certain conditions given by this question. ...
2
votes
0answers
50 views

Computing a “cheap” upper bound on the norm of the solution to a linear system

Consider the linear system $A x = b$, where $A$ is an invertible, $n \times n$, real matrix. I would like to compute a "cheap" upper bound on the (p-)norm of the solution; i.e. $\|x\|_p$. One can, of ...
0
votes
0answers
16 views

final value theorem in the presence of white noise

I apply the final value theorem to get the steady-state error with the presence of white noise and I just keep getting zero. To me, it seems wrong to have zero steady-state error when there is noise ...
0
votes
5answers
53 views

Creative way to solve a linear system

Does anyone know a method for solving the following linear system: Here, $\pi_0, \, \pi_1, \, \pi_2$ are the variables. I tried solving by setting up a simple matrix and row-reducing, but it ...
0
votes
1answer
19 views

How to solve this system of 3 equations with substitution?

I have the system: $$-4 + λ = -3a + at\\ 1+2λ = -a + at\\ 3λ = 3a-at$$ but whenever I try to substitute, I end up getting lots of fractions that are hard to work with. By summing the 2nd and 3rd ...
0
votes
2answers
29 views

Huge linear system of equations with powers of $2$

I've got a large system of equations: $$ \begin{align*} (2^0)^na_n + (2^0)^{n-1}a_{n-1} + \cdots + (2^0)^1a_1 &= 4^0 \\ (2^1)^na_n + (2^1)^{n-1}a_{n-1} + \cdots + (2^1)^1a_1 &= 4^1 \\ \vdots\\ ...
0
votes
3answers
36 views

Can I find the value of $x & y$

Find x,y from N such as $x^{(2y)}=1560-x^{y}$.Is it possible to find the value of x and y only from one equation. please help me.I approached in different ways.But all my attempt went in vain.
1
vote
1answer
24 views

Translating verbal descriptions into algebraic expressions

I'm trying to solve the following problem but the result I'm getting is not logical given the data of the problem. Pat invested a total of \$30,000. Part of the money was invested in a money ...
3
votes
2answers
125 views

Trigonometric equation help is sought

A trigonometric equation is to be solved, the solution ($X=10^\circ$) is very clear but I need a proper method. $$\sin(60^\circ-2X)\sin(5X)=\sin(8X)\sin(3X).$$
0
votes
1answer
47 views

Point Parallel Form Describe Same Line as Point Normal Form

And that's how far I able to get, any suggestion how I can equate both (bold) equation or did I do totally wrong?
1
vote
1answer
22 views

For a linear function, the fiber of the output is the translate of the kernel by the input. (Trivial observation, proof needed.)

As you may already know, I am a newbie to linear algebra. I am supposed to prove that for every linear function between vector spaces, for every input, the fiber of the corresponding output equals the ...
1
vote
1answer
33 views

If we know nullspace of matrix, how to find reduced row echelon form of that matrix?

vectors u = [4 1 0 0] and v = [1 0 2 1] form a base of nullspace of matrix $$ A\in M_{5,4}(R) $$ Find a reduced row echelon form of Matrix A. Since $ n-r = dimN(A) $ we know we got two base ...
1
vote
3answers
41 views

Short question about the homogenous system

I am working on a text book problem for a intro linear course. But the solution is not in the back. I am looking to see if I understand it correctly. The question asks, " If A is a matrix, and the ...
0
votes
1answer
45 views

Solve the linear system by Gauss - Jordan elimination

$$ \begin{align} x& - y + 2z - w &= -1\\ 2x& + y - 2z - 2w &= -2\\ -x& + 2y - 4z + w &= 1\\ 3x& -3w &= -3 \end{align} $$ ...
0
votes
1answer
43 views

Nonhomogeneous Linear Systems and Vector Space Solutions

Are there any nonhomogeneous linear systems with a solution set that forms a vector space? I know that, in order to be a vector space, a set must consists of a set V together with operations + (called ...
0
votes
1answer
43 views

Solve the linear system by Gaussian elimination

$\begin{cases}-2b+3c=1 \\ 3a+6b-3c=-2 \\ 6a+6b+3c=5\end{cases}$ I got an inconsistent linear system with the third row being 0 0 0 6. May someone please verify if I am right? I looked it over.
0
votes
2answers
26 views

Find solutions for an differential equation system

I have a differential equation system $x_1'(t) = -x_2(t)$ $x_2'(t) = -x_1(t)$ I see that I can write $\dot{x} = Ax$ where $A = \begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$ The complete ...
1
vote
1answer
30 views

Rational solutions to a system of equations

I have a system of equations $$\begin{align} xy + 3zw = 0; \\ xz + 2yw = 0; \\ xw + yz = 0. \\ \end{align}$$ Plugging it into a CAS, I see that all the rational solutions to this system have ...
5
votes
4answers
407 views

Linear Algebra - four “true or false” questions about matrices and linear systems

I'm reviewing for my linear algebra course, and have four "true or false" questions that I'm struggling to prove. I've included my approach to the solutions in brackets below them: 1) If $A^2 = B^2$, ...
1
vote
3answers
43 views

System of Linear Equations - how many solutions?

For which real values of t does the following system of linear equations: $$ \left\{ \begin{array}{c} tx_1 + x_2 + x_3 = 1 \\ x_1 + tx_2 + x_3 = 1 \\ x_1 + x_2 + tx_3 = 1 \end{array} \right. $$ ...
1
vote
2answers
63 views

For the following system to be consistent, what must k not be equal to?

$6x - 4y + 4z = 5$ $9x - 6y + kz = -4$ $12x - 8y = -10$ Originally I just multiplied the first row by (3/2) and subtracted it from the second, which gives you a value of 6 for the answer. ...
0
votes
1answer
78 views

Linear Algebra (Ax=B)

I am having some difficulty thinking about a certain concept in my linear notes. I will post below the theorem that is involved, Theorem: Let X$_0$ be a particular solution of the system AX = B ...
0
votes
6answers
310 views

How to solve a system of two linear equations with two unknowns?

How do I solve this system of equations? $$\begin{cases} 7(a+b)=b-a \\4(3a+2b)=b-8\end{cases}$$ Progress I tried both substitution and elimination, but when I set $a$ or $b$ free on one side, I ...
0
votes
1answer
43 views

How to find system of equations from solution space

I have to find homogeneous system of linear equations whose solution space is: V = span((1,-2,4,3),(1,-1,6,4),(3,-8,8,3)). First I found vectors were linearly dependent, so I discarded the third ...
0
votes
0answers
26 views

Solving an equation with boundary conditions to find coefficients

I want to find the unknown constants in the function $f(x,y)=A(e^{-i.k_{x}x}+C_{1}x+C_{2})(e^{-i.k_{y}y}+C_{3}y+C_{4})$, using the following known boundary conditions and auxiliary equation ...
1
vote
0answers
67 views

How to find a linear equation with the same solution set?

I have this homework question that I solved, but it was so easy that I feel like I did something wrong. Can someone just confirm that my approach to this problem was correct? So, I have to find a ...
-2
votes
2answers
32 views

System of linear equation matrix? [duplicate]

How would I do this question. Determine the value(s) of $h$ such that the matrix is augmented of a consistent linear system. My matrix \begin{bmatrix} 1&h&4\\ 3&6&8 \end{bmatrix} I ...
0
votes
3answers
57 views

System of linear equation

Determine the value for k for which the system of linear equation has infinitely many solution. \begin{cases} 2x - y = 2\\ 4x + ky = 4 \end{cases}
3
votes
0answers
40 views

Algorithms for solving overdetermined, homogeneous linear systems with multivariate polynomial coefficients

I would like to solve overdetermined, homogeneous linear systems of equations with multivariate polynomial coefficients, i.e., $Ap=0$ with $A$ an $m\times n$ matrix, $m\gg n$, and $a_{i,j} \in ...
0
votes
0answers
37 views

Solving system of equations in rationals

Do there exist solutions to solve system of $n-2$ equations with $n-2$ variables where $n$ is fixed even integer and $a_i,b,c\in\mathbb{Q},i\in\{0,1,2,\cdots,n-5\}$ $$\left\{ ...
0
votes
2answers
57 views

Substitution vs Elimination in Solving Systems of Equations

When solving systems of equations, is it more efficient in terms of time to solve it using substitution or elimination, and what are your reasons for saying so?
0
votes
1answer
28 views

Transformation of inverse to a system of linear equations

I have $X = (U'WU)^{-1}U'$ to be solved. Suppose $U'$ is $3 \times 7, W$ is $7 \times 7$ positive definite matrix, $U'$ is of rank 3. So, I transformed $(U'WU)^{-1}U'$ as $(U'WU)^{-1}U'WU = I\\ XWU ...
4
votes
4answers
517 views

What is the non-trivial, general solution of these equal ratios? [closed]

Provide non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ $a=?, b=?, c=?$ The solution should be general.
1
vote
2answers
241 views

Matrix Equation- solution

Sir, We have given $A= \begin{bmatrix}q_1 & q_2&q_3 \\ q_4 & q_5&q_6\\ q_7 & q_8&q_9 \end{bmatrix} \tag 1$. A is a matrix with determinant 1,orthogonal , invertible and ...
2
votes
0answers
23 views

Find a reduced echelon basis from a reduced echelon matrix.

The reduced row matrix was this ---> $\begin{pmatrix}1&2&0&1&0\\0&0&1&3&0\\0&0&0&0&1\\0&0&0&0&0&\end{pmatrix} = 0$ So i computed ...
-1
votes
1answer
55 views

Solving Systems of Equations..!! [closed]

I actually don't want to solve the systems of equations. I just want to let them equal each other so I can cancel one of them and solve the other one. Example: $E_1\quad x-y=0$ $E_2\quad 2x-2y=0$ ...
2
votes
0answers
32 views

What is the solution to the system $\frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1}$?

I'm trying to solve the system $$ \begin{matrix} & \frac{df_1}{dt} = kf_1+lf_2 \\ & \vdots \\ & \frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1} \\ & \vdots \\ & \frac{df_N}{dt} = ...
1
vote
3answers
33 views

number of solution to the given equation.

a,b,c, are all non-negative integers such that a + b + c=100 and 1000a + 300b + 50c = 10000 How many such triplets are possible? i have tried to reduce ...
2
votes
1answer
27 views

Can I convert between a rotation about an axis and a rotation according to two angles (all in 3D) without solving a system of nonlinear equations?

I am writing a program that needs to be able to switch between a rotation described by 2 angles to a rotation described an axis and one angle. I found one way to do this from this question, which ...
0
votes
0answers
16 views

Variable bounds of under-determined linear system

If I have a non-negative, under-determined linear system $\mathbf{Ax}=\mathbf{b}$ $\mathbf{x}\geq\mathbf{0}$ is there a fast way to compute the upper and lower bounds on values of each element of ...
6
votes
4answers
91 views

Solve the System of Equations in Real $x$,$y$ and $z$

Solve for $x$,$y$ and $z$ $\in $ $\mathbb{R}$ if $$\begin{align} x^2+x-1=y \\ y^2+y-1=z\\ z^2+z-1=x \end{align}$$ My Try: if $x=y=z$ then the two triplets $(1,1,1)$ and ...
0
votes
0answers
47 views

Underdetermined system of equations

I am sorry in advance if the question I am going to ask is trivial. I have a problem of underdetermined system of equations (6 unknowns and three equations).All unknowns are between 0 and 1. Are there ...
1
vote
1answer
42 views

Solving an augmented coefficient matrix so there are infinitely solutions

I am trying to figure out this math problem. For what values $a,b$ does the linear system have infinitely many solutions? This is the matrix $$ \left[ \begin{array}{ccc|c} ...