Question

If A = `[(2 , -1),(-4, 5)]` and B = [0 -3] find the matrix C such that CA = B

Answer 1

A = `[(2 , -1),(-4, 5)]` and B = [0 -3]
Let matrix C = [x   y]
Since the matrix A is 2 x 2 and B = 7 x 2
∵ CA = B
∴ `(x  y) [(2, -1),(-4, 5)]` = [0 –3]
= (2x – 4y – x + 5y)
= [0 –3]
Comparing,
2x – 4y = 0
⇒ x – 2y = 0
∴ x = 2y
and 
–x + 5y = –3
⇒ –2y + 5y = –3
⇒ 3y = –3
⇒ y = –1
∴ x = 2y
= 2 x (–1)
= –2
Hence C
= [x     y]
= [–2  –1].