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Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 14

Answers (1)

Answer:

 k, a, b = (-6, -4, -9)

Hint:

 Use the basics of scalar matrix.

Given:

 A=\left[\begin{array}{cc} 0 & 2 \\ 3 & -4 \end{array}\right], k A=\left[\begin{array}{cc} 0 & 39 \\ 2 b & 24 \end{array}\right]

Solution:

Given

\begin{aligned} &k A=k\left[\begin{array}{cc} 0 & 2 \\ 3 & -4 \end{array}\right]=\left[\begin{array}{cc} 0 & 2 k \\ 3 k & -4 k \end{array}\right] \\ &{\left[\begin{array}{cc} 0 & 39 \\ 2 b & 24 \end{array}\right]=\left[\begin{array}{cc} 0 & 2 k \\ 3 k & -4 k \end{array}\right]} \end{aligned}

By the comparison,

-4 k=24 k=-6

And

3 a=2 k a=2 \times \frac{(-6)}{3}=-4

Also,

2 b=3 k b=3 \times \frac{-6}{2}=-9

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