Question

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

Answer 1

Given
A = `[(2, -1),(-4, 5)]`

B = `[(-3),(2)]` 

Let martix C = `[(x),(y)]`

∴ AC = `[(2, -1),(-4, 5)][(x),(y)] = [(2x - y),(-4x + 5y)]`
But AC = B
∴ `[(2x - y),(-4x + 5y)] = [(-3),(2)]`
Comparing the corresponding elements
  2x – y = –3                      ...(i)
–4x + 5y = 2                     ...(ii)
Multiplying (i) by 5 and (ii) by 1
10x – 5y = –15
–4x + 5y = 2    
Adding, we get
6x = –13
⇒ x = `(-13)/(6)`
Substituting the value of x in (i)
`2((-13)/6) - y` = –3

⇒ `(-13)/(3) - y` = –3

–y = `–3 + (13)/(3)`

= `(-9 + 13)/(3)`

= `(4)/(3)`

∴ y = `-(4)/(3)`

∴ Matrix C = `[((-13)/6),(-4/3)]`.