0
votes
1answer
27 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 ...
1
vote
0answers
17 views

Verification - Matrices and Linear Equations Part 1

Would just like to verify my Answers and bounce off my ideas and thinking with someone as I feel quite alone in this course. I am usually great at maths and enjoy it but these matrices and linear ...
1
vote
1answer
29 views

Solution to two equations with three unknowns

So I'm a student studying through correspondence and I need some help. This is an assignment question, and I have tried everything I know how, to answer it which has lead me to the conclusion that ...
1
vote
2answers
224 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 ...
0
votes
1answer
13 views

Solution of a matrix equation with a triangular matrix

Given the matrix: $$B = \begin{bmatrix} b_1 & 0 & 0& ... \\[0.3em] b_2 & b_1 &0 & ... \\[0.3em] b_3 & b_2 & b_1 \\... ...
3
votes
1answer
27 views

Find the polynomial function

Anybody knows how to find the polynomial function with evaluated values, where if the degree is $n$ I have $n+1$ values of the function like $f(0) = a_0, f(1) = a_1, \ldots, f(n) = a_n$.
0
votes
0answers
31 views

Converting sums to matrix equations

I am able to transform basic sums to vector/matrix equations. But now I have something like: $$ c_{p,q} = \sum_{n=1}^N \sum_{r=1}^R \sum_{s=1}^S e_n x_{n-q-s,p} \cdot h_{r,s} \cdot g_r \cdot ...
1
vote
0answers
46 views

Solving the equation $AX+XA' = 0$

I am trying to solve the equation $AX + XA' = 0$ I could find how to solve when "$+$" is a "$-$" or $X$ is conjugated instead of $A$. Is there a solution for this problem too? In particular, I am ...
2
votes
1answer
72 views

Method of characteristics for a system of pdes

I can do parts a) and b) as follows $\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1\end{pmatrix}\frac{\partial}{\partial{}x}\begin{pmatrix} u \\ v \\ w\end{pmatrix}+\begin{pmatrix} ...
0
votes
1answer
32 views

Can someone please provide an intuition behind cramer's rule?

See question. I usually get concepts like this very quickly (no studying required), but this one looks like Chinese. Can someone please help me understand a brief intuition behind Cramer's rule for ...
2
votes
2answers
75 views

Simplfy a complex matrix into a real one

I encounter systems of linear complex equations (At most 3 equations) in my circuit analysis course. The calculator I am using is Casio fx-991ES and it only accepts real elements when in matrix or ...
0
votes
0answers
25 views

Is there a non-zero solution to this system of equations?

I have a system of equations. $\mu_1p_1=(1-p_1)\sum_{i=1, i\ne 1}^N \lambda_{i1}p_i$ $\mu_2p_2=(1-p_2)\sum_{i=1, i\ne 2}^N \lambda_{i2}p_i$ and so on. The values $\mu_k$ and $\lambda_{kl}$ are ...
0
votes
0answers
113 views

Matrix equation existence of solutions

In my textbook (Linear Algebra and its applications by David C. Lay) one finds the following theorem: Let A be an $m\times n$ matrix. Then the following statements are logically equivalent: ...