User Grace C

11 votes

6 answers

872 views

Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$.

asked Oct 3, 2012 at 6:01

4 votes

1 answer

769 views

How to solve / set up three equations three unknowns with a matrix?

asked Sep 11, 2012 at 22:25

3 votes

2 answers

3k views

A context-free grammar for the language $L = \{ a^ib^jc^k \space|\space 0 \leq i \leq j \leq i + k \}$

asked Dec 8, 2012 at 4:40

2 votes

2 answers

5k views

Let $B = ${$1-t^2, t-t^2, 2-2t+t^2$}. Check that $B$ is a basis for $P_2$ and find $[3+t-6t^2]_B$

asked Nov 7, 2012 at 7:25

2 votes

2 answers

419 views

A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$

asked Sep 12, 2012 at 5:45

1 vote

2 answers

1k views

How do I determine linear independence when I don't know the values of the vectors?

asked Sep 11, 2012 at 22:56

1 vote

3 answers

9k views

Show that the transformation T defined by $T(x_1, x_2)\; = \;... $ is NOT linear.

asked Sep 12, 2012 at 4:39

1 vote

1 answer

1k views

Need help with Determining a formula for a Resistance using a linear system for loop currents

asked Oct 16, 2012 at 23:05

1 vote

1 answer

2k views

Given a parallelepiped, how do I find the determinant given vertices?

asked Oct 17, 2012 at 5:15

1 vote

2 answers

5k views

Let $M_{2\times 2}$ be the vector space of all $2\times 2$ matrices. Show that the set of non-singular matrices is NOT a subspace.

asked Nov 19, 2012 at 5:01

1 vote

2 answers

4k views

Describe the smallest subspace of $M_{2\times 2}$ that contains matrices...

asked Nov 19, 2012 at 7:57

1 vote

2 answers

2k views

Row Reduction with Cofactor Expansion

asked Dec 9, 2012 at 4:24

1 vote

1 answer

2k views

Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$

asked Nov 7, 2012 at 6:34

0 votes

1 answer

2k views

Find and draw the image of the triangle with vertices (2,1), (1, 2), (2,2)

asked Dec 10, 2012 at 0:42

0 votes

3 answers

26k views

Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$ [duplicate]

asked May 4, 2014 at 9:40

0 votes

2 answers

1k views

Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials...

asked Nov 7, 2012 at 4:14

0 votes

2 answers

3k views

How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions?

asked Nov 7, 2012 at 6:24

0 votes

1 answer

279 views

Determinants of Variables

asked Oct 17, 2012 at 2:10

0 votes

1 answer

1k views

What do I do if I've been asked to find the preimage of a vector, but the inverse of the Transformation Matrix doesn't exist?

asked Oct 3, 2012 at 3:28

-2 votes

2 answers

771 views

Explain why a determinant function is a cubic polynomial

asked Oct 17, 2012 at 7:51

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20 Questions

Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$.

How to solve / set up three equations three unknowns with a matrix?

A context-free grammar for the language $L = \{ a^ib^jc^k \space|\space 0 \leq i \leq j \leq i + k \}$

Let $B = ${$1-t^2, t-t^2, 2-2t+t^2$}. Check that $B$ is a basis for $P_2$ and find $[3+t-6t^2]_B$

A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$

How do I determine linear independence when I don't know the values of the vectors?

Show that the transformation T defined by $T(x_1, x_2)\; = \;... $ is NOT linear.

Need help with Determining a formula for a Resistance using a linear system for loop currents

Given a parallelepiped, how do I find the determinant given vertices?

Let $M_{2\times 2}$ be the vector space of all $2\times 2$ matrices. Show that the set of non-singular matrices is NOT a subspace.

Describe the smallest subspace of $M_{2\times 2}$ that contains matrices...

Row Reduction with Cofactor Expansion

Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$

Find and draw the image of the triangle with vertices (2,1), (1, 2), (2,2)

Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$ [duplicate]

Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials...

How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions?

Determinants of Variables

What do I do if I've been asked to find the preimage of a vector, but the inverse of the Transformation Matrix doesn't exist?

Explain why a determinant function is a cubic polynomial