Advertisements
Advertisements
Question
Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the matrix X.
Solution
We have
`[(2, 1),(-3, 4)], "X" = [(7),(6)]`
Let X = `[(x),(y)]`
So, `[(2, 1),(-3, 4)][(x),(y)] = [(7),(6)]`
⇒ `[(2x + y),(-3x + 4y)] = [(7),(6)]`
2x + y = 7 ...(i)
–3x + 4y = 6 ...(ii)
Multiplying (i) by 3 and (ii) by 2, and adding
we get:
6x + 33y = 21
–6x + 8y = 12
11y = 33
⇒ y = 3
From (i),
2x = 7 – 3
2x = 4
x = 2
So, X = `[(2),(3)]`
APPEARS IN
RELATED QUESTIONS
Find x and y, if `[(x, 0),(-3, 1)][(1, 1),(0, y)] = [(2, 2),(-3, -2)]`
If A = `[(a, 0),(0, 2)]`, B = `[(0, -b),(1, 0)]`, M = `[(1, -1),(1, 1)]` and BA = M2, find the values of a and b.
Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find A2
Solve for x and y: `[(x + y, x - 4)][(-1, -2),(2, 2)] = [-7, -11]`
If `P = [(2,6),(3,9)]` and `Q = [(3,x),(y, 2)]` find x and y such that PQ = null matrix
`[(2sin 30° ,- 2 cos 60°),(- cot 45° , sin 90°)]`
`[(tan 45° , sec 60°),("cosec" 30° , cos 0°)]`
If A = `[(-1, 3),(2, 4)], "B" = [(2, -3),(-4, -6)]` find the matrix AB + BA
If `[(1, 3),(0, 0)] [(2),(-1)] = [(x),(0)]` Find the value of x
If A = `[(2, x),(0, 1)] and "B" = [(4, 36),(0, 1)]`,find the value of x, given that A2 – B
If matrix A = `[(2, 2),(0, 2)]` and A2 = `[(4, x),(0, 4)]`, then the value of x is ______.
