Advertisements
Advertisements
प्रश्न
Answer the following question:
if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A2 – B2 , find x and y
Advertisements
उत्तर
(A + B)(A – B) = A2 – B2
∴ A2 – AB + BA – B2 = A2 – B2
∴ –AB + BA = 0
∴ AB = BA
∴ `[(-3, 2),(2, -4)] [(1, x),(y, 0)] = [(1, x),(y, 0)] [(-3, 2),(2, -4)]`
∴ `[(-3 + 2y, -3x +0),(2 - 4y, 2x + 0)] = [(-3 + 2x, 2 - 4x),(-3y + 0, 2y + 0)]`
∴ By equality of matrices, we get
2 – 4x = – 3x
∴ x = 2
and 2y = 2x
∴ y = x
∴ y = 2
∴ x = 2, y = 2
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.
Show that AB = BA where,
A = `[(costheta, - sintheta),(sintheta, costheta)], "B" = [(cosphi, -sinphi),(sinphi, cosphi)]`
If A = `[(4, 8),(-2, -4)]`, prove that A2 = 0
Verify A(BC) = (AB)C of the following case:
A = `[(2, 4, 3),(-1, 3, 2)], "B" = [(2, -2),(3, 3),(-1, 1)], "C" = [(3, 1),(1, 3)]`
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(1, -1, 3),(2, 3, 2)], "B" = [(1, 0),(-2, 3),(4, 3)], "C" = [(1, 2),(-2, 0),(4, -3)]`
If A = `[(1, -2),(5, 6)], "B" = [(3, -1),(3, 7)]`, Find AB - 2I, where I is unit matrix of order 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),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and if (A + B)2 = A2 + B2 . find values of a and b
Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`
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, z if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)]` = `[("x" - 3),("y" - 1),(2"z")]`
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that `"A"^2=[(cos2alpha, sin2alpha),(-sin2alpha, cos2alpha)]`
Select the correct option from the given alternatives:
If A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______
Select the correct option from the given alternatives:
If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______
Select the correct option from the given alternatives:
If A = `[(-2, 1),(0, 3)]` and f(x) = 2x2 – 3x, then f(A) = ………
Answer the following question:
If f (α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(–α) + f(α)
Answer the following question:
If Aα = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that Aα . Aβ = Aα+β
Answer the following question:
If A = `[(3, -5),(-4, 2)]`, show that A2 – 5A – 14I = 0
Answer the following question:
If A = `[(2, -1),(3, -2)]`, find A3
Answer the following question:
Find x, y if, `[(0, -1, 4)]{2[(4, 5),(3, 6),(2, -1)] + 3[(4, 3),(1, 4),(0, -1)]} = [(x, y)]`
Answer the following question:
Find x, y if, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`
Answer the following question:
Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
Answer the following question:
Find x, y, z if `{[(1, 3, 2),(2, 0, 1),(3, 1, 2)] + 2[(3, 0, 2),(1, 4, 5),(2, 1, 0)]} [(1),(2),(3)] = [(x),(y),(z)]`
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)]` and I is the unit matrix of order 3, then A2 + 2A4 + 4A6 is equal to ______.
