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CBSE Class 12 · 2005 · MatricesVery Short Answer

If

A = [23 - 1 2]

and

B = [0 - 1 47]

, find

3 A^{2} - 2 B + I

.

Answer: $[438 - 20 - 10]$ \,

Solution

First square

A

:

A^{2} = [23 - 1 2] [23 - 1 2] = [112 - 4 1] .

Then

3 A^{2} = [336 - 12 3]

and

2 B = [0 - 2 814]

.

3 A^{2} - 2 B + I = [336 - 12 3] - [0 - 2 814] + [1001] = [438 - 20 - 10] .

The booklet key shows

- 4

in the

(1, 2)

entry, but the

(1, 2)

entry of

A^{2}

is

2 (- 1) + (- 1) (2) = - 4

, giving

3 (- 4) - 8 = - 20

; the value above is correct.

CBSE Class 12 Board · 2005 · Subjective

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