# write B as a linear combination of the other matrices, if possible. B=[[2,-2,3],[0,0,-2],[0,0,2]] A_1=[[1,0,0],[0,1,0],[0,0,1]] A_2=[[0,1,1],[0,0,1],[0,0,0]] A_3=[[-1,0,-1],[0,1,0],[0,0,-1]] A_4=[[1,-1,1],[0,-1,-1],[0,0,1]]

Question
Matrices
write B as a linear combination of the other matrices, if possible.
$$B=[[2,-2,3],[0,0,-2],[0,0,2]]$$
$$A_1=[[1,0,0],[0,1,0],[0,0,1]]$$
$$A_2=[[0,1,1],[0,0,1],[0,0,0]]$$
$$A_3=[[-1,0,-1],[0,1,0],[0,0,-1]]$$
$$A_4=[[1,-1,1],[0,-1,-1],[0,0,1]]$$

2021-01-14

### Relevant Questions

write B as a linear combination of the other matrices, if possible.
$$B=\begin{bmatrix}2 & 3 \\-4 & 2 \end{bmatrix} , A_1=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &-1 \\1 & 0 \end{bmatrix} , A_3=\begin{bmatrix}1 &1 \\0 & 1 \end{bmatrix}$$
write B as a linear combination of the other matrices, if possible.
$$B=\begin{bmatrix}2 & 5 \\0 & 3 \end{bmatrix} , A_1=\begin{bmatrix}1 & 2 \\-1 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &1 \\2 & 1 \end{bmatrix}$$
Find the general form of the span of th e indicated matrices, span(A1, A2)
$$B=\begin{bmatrix}2 & 5 \\ 0 & 3 \end{bmatrix} , A_1=\begin{bmatrix}1 & 2 \\ -1 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 & 1 \\ 2 & 1 \end{bmatrix}$$
Let B be a $$4 \times 4$$ 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 (so that the column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product ABC (same B) of three matrices.
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.
Compute the indicated matrices, if possible .
A^2B
let $$A=\begin{bmatrix}1 & 2 \\3 & 5 \end{bmatrix} \text{ and } B=\begin{bmatrix}2 & 0 & -1 \\3 & -3 & 4 \end{bmatrix}$$
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
$$A=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix} , B=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}$$
compute the indicated matrices (if possible). D+BC
Let $$A=\begin{bmatrix}3 & 0 \\ -1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 1 \\ 0 & 2 &3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 &6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\ -2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} , F=\begin{bmatrix}-1 \\ 2 \end{bmatrix}$$
Find if possible the matrices:
a) AB b) BA.
$$A=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix} , B=\begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$
compute the indicated matrices (if possible). B - C
Let
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\3 & 4\\5&6 \end{bmatrix}, D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix},E=\begin{bmatrix}4 & 2 \end{bmatrix},F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$
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