Advertisements
Advertisements
प्रश्न
If A = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)],"B" = [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`, state whether AB = BA? Justify your answer.
उत्तर
AB = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)] [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`
= `[(-2+ 3 + 1, -1 + 0 + 2, -4 + 2 + 1),(4 + 9 + 0, 2 + 0 + 0, 8 + 6 + 0),(2 - 9 + 1, 1 + 0 + 2, 4 - 6 + 1)]`
∴ AB = `[(2, 1, -1),(13, 2, 14),(-6, 3, -1)]` ...(i)
BA = `[(2, 1, 4),(3, 0, 2),(1, 2, 1)][(-1, 1, 1),(2, 3, 0),(1, -3, 1)]`
= `[(-2 + 2 + 4, 2 + 3 - 12, 2 + 0 + 4),(-3 + 0 + 2, 3 + 0 - 6, 3 + 0 + 2),(-1 + 4 + 1, 1 + 6 - 3, 1 + 0 + 1)]`
∴ BA = `[(4, -7, 6),(-1, -3, 5),(4, 4, 2)]` ...(ii)
From (i) and (ii), we get
AB ≠ BA.
APPEARS IN
संबंधित प्रश्न
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 = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, show that A2 – 4A is a scalar matrix.
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 and y, if `{4[(2, -1, 3),(1, 0, 2)] - [(3, -3, 4),(2, 1, 1)]}[(2),(-1),(1)] = [(x),(y)]`
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 = `[(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 = `[(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 = `[(1, 2),(-1, 3)]`, then find A3.
State whether the following statement is True or False:
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, then AT = A
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
