Carol Gates
2021-01-13
Answered

write B as a linear combination of the other matrices, if possible.

$B=[[2,-2,3],[0,0,-2],[0,0,2]]$

${A}_{1}=[[1,0,0],[0,1,0],[0,0,1]]$

${A}_{2}=[[0,1,1],[0,0,1],[0,0,0]]$

${A}_{3}=[[-1,0,-1],[0,1,0],[0,0,-1]]$

${A}_{4}=[[1,-1,1],[0,-1,-1],[0,0,1]]$

You can still ask an expert for help

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

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

asked 2021-02-08

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.

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.

asked 2021-02-20

Compute the product AB by the definition of the product of matrices, where $A{b}_{1}\text{and}A{b}_{2}$ are computed separately, and by the row-column rule for computing AB.

$A=\left[\begin{array}{cc}-1& 2\\ 2& 5\\ 5& -3\end{array}\right],B=\left[\begin{array}{cc}4& -1\\ -2& 4\end{array}\right]$

Determine the product AB

AB=?

Determine the product AB

AB=?

asked 2021-02-25

Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

asked 2021-03-07

a) List all possible Jordan forms for $3\times 3$ matrices.

c) List all possible Jordan forms for$4\times 4$ matrices.

c) List all possible Jordan forms for

asked 2021-01-04

Find the inverse of the transformation $x\text{'}=2x-3y,y\text{'}=x+y$, that is, find $x,y$ in terms of $x\text{'},y\text{'}.$ (Hint: Use matrices.) Is the transformation orthogonal?

asked 2021-01-10

Use a system of linear equations to find the quadratic function

$f(x)=a{x}^{2}2+bx+c$

that satisfies the given conditions. Solve the system using matrices.

f(-2) = 6, f(1) = -3, f(2) = -14

f(x) =?

that satisfies the given conditions. Solve the system using matrices.

f(-2) = 6, f(1) = -3, f(2) = -14

f(x) =?