If [{a -1 5} {b 3 -4}] [{4 3} {1 0} {7 -6}] = [{34 -30} {-1 42}], then (a, b) is equal to

Question

If \(\begin{bmatrix}a& - 1&5\\b&3&-4 \end{bmatrix} \begin{bmatrix}4&3\\1&0\\7&-6 \end{bmatrix} = \begin{bmatrix}34&-30\\-1&42\end{bmatrix}\), then (a, b) is equal to 

(a) (1, 3)

(b) (–2, 4)

(c) (0, 6)

(d) (2, –3)

Answer 1

Correct option is (c) (0, 6)

Equating corresponding elements we have 

4a + 34 = 34

⇒ a = 0

4b - 25 = -1

⇒ 4b = 24

⇒ b = 6

and 

3a - 30 = -30

⇒ a = 0

3b + 24 = 42

⇒ 3b = 18

⇒ b = 6

\(\therefore\) a = 0, b = 6.