Advertisements
Advertisements
Question
If A = `[(3, 3),(p, q)]` and A2 = 0 find p and q
Solution
Given
A = `[(3, 3),(p, q)]`
A2 = A x A = `[(3, 3),(p, q)][(3, 3),(p, q)]`
= `[(9 + 3p, 9 + 3q),(3p + pq, 3p + q^2)]`
But A2 = 0
∴`[(9 + 3p, 9 + 3q),(3p + pq, 3p + q^2)] = [(0, 0),(0, 0)]`
Comparing the corresponding elements
9 + 3p = 0
⇒ 3p = –9
⇒ p = –3
9 + 3q = 0
⇒ 3q = –9
⇒ q = –3
Hence p = –3, q = –3.
APPEARS IN
RELATED QUESTIONS
if A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`, find AC + B2 – 10C.
Find the value of x, given that A2 = B,
A = `[(2, 12),(0, 1)]` and B = `[(4, x),(0, 1)]`
If `A = [(2, 5),(1, 3)]`, `B = [(4, -2),(-1, 3)]` and I is Identity matrix of same order and `A^t` is the transpose of matrix A find `A^t.B + BI`
Given `[["4 " " 2" ],[" -1 "" 1 " ]]` M = 6I , where M is a matrix and I is unit matrix of order 2×2.
(i) State the order of matrix M.
(ii) Find the matrix M.
If A = [4 7] and B = [3 l], find: A - B
If P = (8 , 5),(7 , 2) , find Pt
Solve for x and y `[(-2,0), (3,1)][(-1), (2x)] +3[(-2), (1)] =2[(y), (3)]`
If A = `[(2, -1),(-4, 5)] and "B" = [(-3),(2)]` find the matrix C such that AC = B
Find a, b, c and d if `3[(a, b),(c, d)] = [(4, a + b),(c + d, 3)] + [(a, 6),(-1, 2d)]`
If A = `[(3/5, 2/5),(x, y)]` and A2 = I, find x,y
