If P = (2 , 9),(5 , 7) and Q = (7 , 3)(4 , 1) , Find 2p + 3q - Mathematics

If P = `|(2 , 9),(5 , 7)|` and Q = `|(7 , 3),(4 , 1)|` , find 2P + 3Q

Sum

`= |(2 , 9),(5 , 7)|_(2 xx 2)` , Q = `|(7 , 3),(4 , 1)|_(2 xx 2)`

2P + 3Q = `|(4 , 18),(10 , 14)| + |(21 , 9),(12 , 3)|`

`= |(4 + 21 , 18 + 9),(10 + 12 , 14 + 3)| = |(25 , 27),(22 , 17)|_(2 xx 2)`

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Chapter 11: Matrices - Exercise 11.1

Chapter 11 Matrices
Exercise 11.1 | Q 7.1

if A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`, find AC + B² – 10C.

If A and B are any two 2 × 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

If A = `[(4, 2),(1,1)]`, find (A – 2I)(A – 3I).

Given A = `[(2, -1),(2, 0)]`, B = `[(-3, 2),(4, 0)]` and C = `[(1, 0),(0, 2)]`, find the matrix X such that : A + X = 2B + C.

Evaluate the following :

`|(2 , -5),(0 , -3)| |(1 , -1),(3 , 2)|`

Given that A = `[(3, 0),(0, 4)]` and B = `[(a, b),(0, c)]` and that AB = A + B, find the values of a, b and c.

If A = `[(9 , 1),(5 , 3)]` and B = `[(1 , 5),(7 , -11)]`, find matrix X such that 3A + 5B - 2X = 0.

If `"A" = [(1 , 2),(-2 , 3)], "B" = [(2 , 1),(2 , 3)] "C" = [(-3 , 1),(2 , 0)]` verify that
A(B + C) = AB + AC.

Find the values of x, y, a and b if `[(x - 2, y),(a + 2b, 3a - b)] = [(3, 1),(5, 1)]`

Given matrix, X = `[(1, 1),(8, 3)]` and I = `[(1, 0),(0, 1)]`, prove that X² = 4X + 5I