SATHEE: Matrices and Determinants 3 Question 4

Matrices and Determinants 3 Question 4

5. If $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$ , then adj $(3 A^{2} + 12 A)$ is equal to

(a) $[\begin{matrix} 72 & - 84 \\ - 63 & 51 \end{matrix}]$

(b) $[\begin{matrix} 51 & 63 \\ 84 & 72 \end{matrix}]$

(d) $[\begin{matrix} 72 & - 63 \\ - 84 & 51 \end{matrix}]$

(2017 Main)

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Answer:

Correct Answer: 5. (b)

Solution:

We have, $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$

$\begin{aligned} ∴ A^{2} = A \cdot A = [\begin{array}{c} 2 & - 3 & 2 & - 3 \\ - 4 & 1 & - 4 & 1 \end{array}] \\ = [\begin{array}{c} 4 + 12 & - 6 - 3 \\ - 8 - 4 & 12 + 1 \end{array}] \\ = [\begin{array}{c} 16 & - 9 \\ - 12 & 13 \end{array}] \end{aligned}$

Now, $3 A^{2} + 12 A = 3 [\begin{matrix} 16 & - 9 \\ - 12 & 13 \end{matrix}] + 12 [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$

$\begin{aligned} = [\begin{array}{c} 48 & - 27 \\ - 36 & 39 \end{array}] + [\begin{array}{c} 24 & - 36 \\ - 48 & 12 \\ 72 & - 63 \end{array}] \\ = [\begin{array}{c} - 84 & 51 \end{array}] \end{aligned}$

$∴ adj (3 A^{2} + 12 A) = [\begin{matrix} 51 & 63 \\ 84 & 72 \end{matrix}]$

Matrices and Determinants 3 Question 4

5. If $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$ , then adj $(3 A^{2} + 12 A)$ is equal to

Answer:

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Matrices and Determinants 3 Question 4

5. If A=[2−3−41], then adj (3A2+12A) is equal to

Answer:

Engineering Preparation

Medical Preparation

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Syllabus

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5. If $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$ , then adj $(3 A^{2} + 12 A)$ is equal to