Let the matrix A,B, C and D be as given. Find the product of the sum of A and B and the difference between C and D. A=begin{bmatrix}1 & 0 0 & 1 end{bmatrix},B=begin{bmatrix}1 & 0 0 & -1 end{bmatrix},C=begin{bmatrix}-1 & 0 0& 1 end{bmatrix},D=begin{bmatrix}-1 & 0 0 & -1 end{bmatrix}

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

Describe all skew symmetric scalar matrices.

Determine whether each statement is sometimes, always , or never true for matrices A and B and explain your reasoning. Stuck on one of them? Try a few examples.
a) If A+B exists , then A-B exists
b) If A and B have the same number of elements , then A+B exists.

Find the inverse of the transformation \(x=

Find the characteristic polynomial of the matrices
$\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]$

The diagram below shows 3 vectors which sum to zero, all ofequal length. What statement would this diagram give?