If A is a 2 × 2 matrix with |A| = 3, use the properties ofdeterminants to compute the following determinants.(а) |2A|(f) |4A¬||If A and B are 3 × 3 matrices and Apute the following determinants.(а) |АB(d) |3A²B|— 3, В 3D 2, сom-(e) |2AB¯||

Answered: If A is a 2 × 2 matrix with |A| = 3,…

If A is a 2 × 2 matrix with |A| = 3, use the properties of determinants to compute the following determinants. (a) |2A| (f) |4A¯'|

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.6: Solve Systems Of Equations Using Determinants

Problem 4.93TI: Evaluate the determinant |324012231| , by expanding by minors along the first row.

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Question

100%

If A is a 2 × 2 matrix with |A| = 3, use the properties of
determinants to compute the following determinants.
(а) |2A|
(f) |4A¬||
If A and B are 3 × 3 matrices and A
pute the following determinants.
(а) |АB
(d) |3A²B|
— 3, В 3D 2, сom-
(e) |2AB¯||

Expert Solution

Step 1

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Given $A$ is a $2 \times 2$ matrix with $|A| = 3$

$(a)$ We have to compute $|2 A|$ .

Use property of determinant, If $A$ be a $n \times n$ matrices then $|k A| = k^{n} |A|$ , where $k$ is a constant.

Here, $A$ is a $2 \times 2$ matrix.

Hence,

$\begin{matrix} |2 A| = 2^{2} |A| \\ = 4 (3) (U s e |A| = 3) \\ = 12 \end{matrix}$

Hence, $|2 A| = 12$ .

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