If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det

Tazmin Horton
2020-11-07
Answered

If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det

You can still ask an expert for help

FieniChoonin

Answered 2020-11-08
Author has **102** answers

Step 1

To solve this problem, we use the standard result of matrix

Ans: We know that

and

Step 2

Ans : Given that

Jeffrey Jordon

Answered 2022-01-27
Author has **2495** answers

Answer is given below (on video)

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 2021-02-09

1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?

asked 2021-01-25

Suppose that $\left[\begin{array}{cccc}4& A& 2& 4\\ -7& -4& -4& B\end{array}\right]+\left[\begin{array}{cccc}0& 7& C& 2\\ 3& D& 4& -7\end{array}\right]=\left[\begin{array}{cccc}4& 3& 10& 6\\ -4& -5& 0& -4\end{array}\right]$

What are the values of A,B,C and D ?

What are the values of A,B,C and D ?

asked 2022-09-09

Use the relation $|AB|=|A||B|$ to show that

$$({a}_{1}^{2}+{a}_{2}^{2})({b}_{1}^{2}+{b}_{2}^{2})=({a}_{1}{b}_{1}-{a}_{2}{b}_{2}{)}^{2}+({a}_{2}{b}_{1}+{a}_{1}{b}_{2}{)}^{2}.$$

$$({a}_{1}^{2}+{a}_{2}^{2})({b}_{1}^{2}+{b}_{2}^{2})=({a}_{1}{b}_{1}-{a}_{2}{b}_{2}{)}^{2}+({a}_{2}{b}_{1}+{a}_{1}{b}_{2}{)}^{2}.$$

asked 2021-02-02

If $A=\left(\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right)\text{and}B=\left(\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right)$ ,then find the matrix X such that $2A+3X=5B$

asked 2020-11-08

If $A=\left[\begin{array}{ccc}1& 2& 0\\ 1& 1& 0\\ 1& 4& 0\end{array}\right],B=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& -1\\ 2& 2& 2\end{array}\right]\text{and}C=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& -1\\ 1& 1& 1\end{array}\right]$ . Show that $AB=AC\text{but}B\ne C$