Question

A,B,C are 3 times 3 matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is det(A^2BC^{-1})? -3 -18 18 -108 36

Matrices
ANSWERED
asked 2020-11-10
A,B,C are \(3 \times 3\) matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is \(det(A^2BC^{-1})\)?
-3
-18
18
-108
36

Answers (1)

2020-11-11
Step 1
Given A, B and C are \(3 \times 3\) matrices.
and
\(|A|=-3\)
\(|B|=-2\)
\(|C|=6\)
Find the determinant of \((A^2BC^{-1})\)
Step 2
since,
\(|AB|=|A| \cdot |B|\)
\(|A^n|=|A|^n\)
and
\(|A^{-1}|=\frac{1}{|A|}\)
Then,
\(|A^2BC^{-1}|=|A^2||B||C^{-1}|\)
\(=|A^2||B| \times \frac{1}{|C|}\)
Substitute all the given values,
Step 3
\(|A^2BC^{-1}|=(-3)^2(-2) \times \frac{1}{6}\)
\(=9 \times (-2) \times \frac{1}{6}\)
\(=-18 \times \frac{1}{6}\)
\(=-3\)
Hence,
\(|A^2BC^{-1}|=-3\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-02-21

A,B,C are \(3 \times 3\) matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is \(det(A^TA^{-1})\)?
1
-9
3
-1
9

asked 2020-11-07

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

asked 2021-05-04

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
asked 2020-12-25

The \(2 \times 2 \) matrices A and B below are related to matrix C by the equation: \(C=3A-2B\). Which of the following is matrix C.
\(A=\begin{bmatrix}3 & 5 \\-2 & 1 \end{bmatrix} B=\begin{bmatrix}-4 & 5 \\2 & 1 \end{bmatrix}\)
\(\begin{bmatrix}-1 & 5 \\2 & 1 \end{bmatrix}\)
\(\begin{bmatrix}-18 & 5 \\10 & 1 \end{bmatrix}\)
\(\begin{bmatrix}18 & -5 \\-10 & -1 \end{bmatrix}\)
\(\begin{bmatrix}1 & -5 \\-2 & -1 \end{bmatrix}\)

...