profesorluissp
2022-09-13
Answered

Is M unique given $A={M}^{2}$ where A and M are real matrices? My guessing is they are unique as I tried to diagonalize A to $PD{P}^{-1}$ and no matter how I order the eigenvalues in D, it still gives the same $M=P{D}^{\frac{1}{2}}{P}^{-1}$. But I am not sure this is true in general, since the diagonalization is too specific.

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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 2021-01-31

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 2020-11-23

Given the matrices $A=\left[\begin{array}{cc}-2& 5\\ -5& -5\end{array}\right]\text{and}B=\left[\begin{array}{c}-5\\ 2\end{array}\right]$
AB=?

asked 2020-12-16

Multiply the following matrices:

$A=\left[\begin{array}{ccc}-2& 1& 5\\ 1& 4& -5\end{array}\right]B=\left[\begin{array}{cc}-1& 7\\ 2& -2\\ 3& 4\end{array}\right]$
AB=?

asked 2021-02-11

Simplify

1)$\left[\begin{array}{cc}4& 5\end{array}\right]+\left[\begin{array}{cc}6& -4\end{array}\right]$

2)$\left[\begin{array}{cc}4& -1\\ 3& 3\\ -5& -4\end{array}\right]-\left[\begin{array}{cc}4& -2\\ 3& 6\\ -5& -6\end{array}\right]$

3)$\left[\begin{array}{cc}4& -1\\ 6& -3\end{array}\right]+\left[\begin{array}{cc}5& -6\\ 5& -5\end{array}\right]-\left[\begin{array}{cc}-2& 0\\ -2& -6\end{array}\right]$

Solve for x and y

$\left[\begin{array}{cc}-10& -4\\ x& -1\end{array}\right]+\left[\begin{array}{cc}-5& 8\\ y& -10\end{array}\right]=\left[\begin{array}{cc}-15& x\\ 16& -11\end{array}\right]$

1)

2)

3)

Solve for x and y

asked 2022-09-14

How can I obtain the generic matrix T such that $\hat{X}=TX$ with:

$$\hat{X}=\left[\begin{array}{cc}a& 0\\ 0& b\\ c& 0\\ 0& d\end{array}\right]$$

and

$$X=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$$

I did several try without obtaining the result I needed.

$$\hat{X}=\left[\begin{array}{cc}a& 0\\ 0& b\\ c& 0\\ 0& d\end{array}\right]$$

and

$$X=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$$

I did several try without obtaining the result I needed.

asked 2021-03-09

Use the graphing calculator to solve if possible

Find the value in row 2 column 3 of