Advertisements
Advertisements
Question
If A = `[(3, 1),(1, 5)]` and B = `[(1, 2),(5, -2)]`, then verify |AB| = |A||B|
Solution
AB = `[(3, 1),(1, 5)] [(1, 2),(5, -2)]`
= `[(3 + 5, 6 - 2),(1 + 25, 2 - 10)]`
= `[(8, 4),(26, -8)]`
∴ AB = `|(8, 4),(26, 8)|`
= – 64 – 104
= – 168
|A| = `|(3, 1),(1, 5)|`
= 15 – 1
= 14
|B| = `|(1, 2),(5, -2)|`
= – 2 – 10
= – 12
∴ |A| |B| = 14(– 12) = – 168
∴ |AB| = |A| |B|
APPEARS IN
RELATED QUESTIONS
Evaluate : `[2 - 1 3][(4),(3),(1)]`
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 = `[(1, 0),(-1, 7)]`, find k, so that A2 – 8A – kI = O, where I is a 2 × 2 unit and O is null matrix of order 2.
Find k, if A = `[(3, -2),(4, -2)]` and A2 = kA – 2I.
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.
Choose the correct alternative.
If A and B are square matrices of order n × n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true?
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, 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 = `[(1, 2),(-1, 3)]`, then find A3.
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 = `[(1, -2),(5, 3)]`, B = `[(1, -3),(4, -7)]`, then A – 3B = ______
If A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`, then verify (BA)T = ATBT
