Advertisements
Advertisements
प्रश्न
Find x and y, if `{4[(2, -1, 3),(1, 0, 2)] - [(3, -3, 4),(2, 1, 1)]}[(2),(-1),(1)] = [(x),(y)]`
उत्तर
`{4[(2, -1, 3),(1, 0, 2)] - [(3, -3, 4),(2, 1, 1)]}[(2),(-1),(1)] = [(x),(y)]`
∴ `{[(8, -4, 12),(4, 0, 8)] - [(3, -3, 4),(2, 1, 1)]}[(2),(-1),(1)] = [(x),(y)]`
∴ `[(8 - 3, -4 + 3, 12 - 4),(4 - 2, 0 - 1, 8 - 1)][(2),(-1),(1)] = [(x),(y)]`
∴ `[(5,-1, 8),(2, -1, 7)][(2),(-1),(1)] = [(x),(y)]`
∴ `[(10 + 1 + 8),(4 + 1 + 7)] = [(x),(y)]`
∴ `[(19),(12)] = [(x),(y)]`
∴ By equality of matrices, we get
x = 19 and y = 12.
APPEARS IN
संबंधित 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.
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.
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 = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (A + 2BT)T = AT + 2B.
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.
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 = `[(1, -2),(5, 3)]`, B = `[(1, -3),(4, -7)]`, then A – 3B = ______
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|
