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Matrices

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Question : 27 of 36

Marks: +1, -0

If

A = \begin{bmatrix} 1 & 4 \\ 3 & 5 \end{bmatrix}

B = \begin{bmatrix} 3 & 0 \\ 4 & 1 \end{bmatrix}

\left| AB \right|

21
$-21$
12
11

Solution:

Concept:

The determinant of a product of two matrices equals the product of their determinants:

|AB| = |A| \cdot |B|

.

Explanation:

First, find

|A|

for

A = \begin{bmatrix} 1 & 4 \\ 3 & 5 \end{bmatrix}

.

|A| = (1)(5) - (4)(3) = 5 - 12 = -7

.

Next, find

|B|

for

B = \begin{bmatrix} 3 & 0 \\ 4 & 1 \end{bmatrix}

.

|B| = (3)(1) - (0)(4) = 3 - 0 = 3

.

Then

|AB| = |A| \cdot |B| = (-7) \cdot 3 = -21

.

Answer:

-21

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