Advertisements
Advertisements
Question
Solve the following :
if A = `[(1, 2),(-1, 3)]`, then find A3.
Solution
A2 = A · A = `[(1, 2),(-1, 3)][(1, 2),(-1, 3)]`
= `[(1 - 2, 2 + 6),(-1 - 3, -2 + 9)]`
∴ A2 = `[(-1, 8),(-4, 7)]`
∴ A3 = A2 · A = `[(-1, 8),(-4, 7)][(1, 2),(-1, 3)]`
= `[(-1 - 8, -2 + 24),(-4 - 7, -8 + 21)]`
∴ A3 = `[(-9, 22),(-11, 13)]`.
APPEARS IN
RELATED QUESTIONS
Show that AB = BA, where A = `[(-2, 3, -1),(-1, 2, -1),(-6, 9, -4)],"B" = [(1, 3, -1),(2, 2, -1),(3, 0, -1)]`.
If A + I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I).
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is a 2 x 2 unit matrix.
Find x and y, if `{4[(2, -1, 3),(1, 0, 2)] - [(3, -3, 4),(2, 1, 1)]}[(2),(-1),(1)] = [(x),(y)]`
Find x, y, x, if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)] = [(x - 3),(y - 1),(2z)]`.
Jay and Ram are two friends. Jay wants to buy 4 pens and 8 notebooks, Ram wants to buy 5 pens and 12 notebooks. The price of one pen and one notebook was ₹ 6 and ₹ 10 respectively. Using matrix multiplication, find the amount each one of them requires for buying the pens and notebooks.
Solve the following :
If A = `[(2, 5),(3, 7)], "B" = 4[(1, 7),(-3, 0)]`, find matrix A – 4B + 7I, where I is the unit matrix of order 2.
Solve the following :
If A = `[(1, 5),(7, 8),(9, 5)], "B" = [(2, 4),(1, 5),(-8, 6)] "C" = [(-2, 3),(1, -5),(7, 8)]` then show that (A + B) + C = A + (B + C).
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (A + 2BT)T = AT + 2B.
Solve the following :
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)],"B" = [(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, then show that AB and BA are bothh singular martices.
Solve the following :
If A = `[(2, -1),(-1, 2)]`, then show that A2 – 4A + 3I = 0.
Solve the following :
If A = `[(-3, 2),(2, 4)], "B" = [(1, "a"), ("b", 0)]` and (A + B) (A – B) = A2 – B2, find a and b.
Solve the following :
If A = `[(2, -4),(3, -2),(0, 1)], "B" = [(1, -1, 2),(-2, 1, 0)]`, then show that (AB)T = BTAT.
If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`, then |AB| = ______
If matrix form of given equations 3x – y = 1 and y + 4x = 6 is AX = B, then A = ______
If A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`, then verify (BA)T = ATBT
If A = `[(3, 1),(1, 5)]` and B = `[(1, 2),(5, -2)]`, then verify |AB| = |A||B|
