Advertisements
Advertisements
प्रश्न
Solve the following :
If A = `[(2, -4),(3, -2),(0, 1)], "B" = [(1, -1, 2),(-2, 1, 0)]`, then show that (AB)T = BTAT.
उत्तर
AB = `[(2, -4),(3, -2),(0, 1)] [(1, -1, 2),(-2, 1, 0)]`
= `[(2 + 8, -2 - 4, 4 + 0),(3 + 4, -3 - 2, 6 - 0),(0 - 2, 0 + 1, 0 + 0)]`
= `[(10, -6, 4),(7, -5, 6),(-2, 1, 0)]`
∴ (AB)T = `[(10, 7, -2),(-6, -5, 1),(4, 6, 0)]` ...(i)
Now,AT = `[(2, 3, 0),(-4, -2, 1)] "and B"^"T" = [(1, -2),(-1, 1),(2, 0)]`
∴ BTAT = `[(1, -2),(-1, 1),(2, 0)] [(2, 3, 0),(-4, -2, 1)]`
= `[(2 + 8, 3 + 4, 0 - 2),(-2 - 4, -3 - 2, 0 + 1),(4 - 0, 6 - 0, 0 + 0)]`
∴ BTAT = `[(10, 7, -2),(-6, -5, 1),(4, 6, 0)]` ...(ii)
From (i) and (ii), we get
(AB)T = BTAT.
APPEARS IN
संबंधित प्रश्न
Evaluate : `[(3),(2),(1)][2 -4 3]`
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)]`.
Verify A(BC) = (AB)C, if A = `[(1, 0, 1),(2, 3, 0),(0, 4, 5)], "B" = [(2, -2),(-1, 1),(0, 3)] and "C" = [(3,2,-1), (2,0,-2)]`
If A = `[(4, 3, 2),(-1, 2, 0)],"B" = [(1, 2),(-1, 0),(1, -2)]` show that matrix AB is non singular.
If A + I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I).
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, show that A2 – 4A is a scalar matrix.
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is a 2 x 2 unit matrix.
Find k, if A = `[(3, -2),(4, -2)]` and A2 = kA – 2I.
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.
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 = `[(3, 1),(1, 5)], "B" = [(1, 2),(5, -2)]`, verify |AB| = |A| |B|.
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 = `[(1, 2),(-1, 3)]`, then find A3.
If A = `[(1, -2),(5, 3)]`, B = `[(1, -3),(4, -7)]`, then A – 3B = ______
