Find the values of $a$ and $b$ for which the following holds: $$\left[\begin{array}{cc} a & b \\ -a & 2b \end{array}\right]\left[\begin{array}{c} 2 \\ -1 \end{array}\right]=\left[\begin{array}{c} 5 \\ 4 \end{array}\right]$$

CBSE Class 12 · 2005 · MatricesVery Short Answer

Find the values of

a

and

b

for which the following holds:

[a - a b 2 b] [2 - 1] = [54]

Answer: $a = 1, b = - 3$

Carry out the matrix multiplication on the left; the product is a

2 \times 1

column matrix.

[2 a - b - 2 a - 2 b] = [54]

Equate corresponding entries, because two matrices are equal only when every entry matches.

2 a - b = 5, - 2 a - 2 b = 4 \Rightarrow a + b = - 2

Add

2 a - b = 5

a + b = - 2

to eliminate

b

3 a = 3

, hence

a = 1

, and then

b = - 2 - a = - 3

a = 1, b = - 3

CBSE Class 12 Board · 2005 · Subjective