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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.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

$$\begin{gathered} {\displaystyle \text{List five vectors in Span }\{{\mathbf{v}}_1,{\mathbf{v}}_2\}\text{ For each vector, show the weights on }} \\ {\mathbf{v}}_1\text{ and }{\mathbf{v}}_2\text{ used to generate the vector and list the three entries of the vector. Do not make a sketch.} \end{gathered}$$

Find x such that the matrix is equal to its own inverse.
$A=\left[\begin{array}{cc}7& x\\ -8& -7\end{array}\right]$

Write the set in the form {x|P(x)}, where P(x) is a property that described the elements of the set. {a,e,i,o,u}.

Given the matrices
$A=\left[\begin{array}{cc}-1& 3\\ 2& -1\\ 3& 1\end{array}\right]\text{ and }B=\left[\begin{array}{cc}0& -2\\ 1& 3\\ 4& -3\end{array}\right]$ find the $3\times 2$ matrix X that is a solution of the equation. 8X+A=B

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1),(1, 1),(1, 2),(2, 0),(2, 2),(3, 0). Find reflexive, symmetric and transitive closure of R.