Advertisements
Advertisements
प्रश्न
Show that AB = BA where,
A = `[(costheta, - sintheta),(sintheta, costheta)], "B" = [(cosphi, -sinphi),(sinphi, cosphi)]`
Advertisements
उत्तर
AB = `[(costheta, -sintheta),(sintheta, costheta)] [(cosphi, -sinphi),(sinphi, cosphi)]`
`= [(costhetacosphi - sintheta sinphi, -costhetasinphi - sinthetacosphi),(sinthetacosphi + costhetasinphi, -sinthetasinphi + costhetacosphi)]`
`= [(cos (theta + phi) - sin (theta + phi)), (sin (theta + phi) cos (theta + phi))]` ...(i)
BA = `[(cosphi, -sinphi),(sinphi, cosphi)] [(costheta, - sintheta),(sintheta, costheta)]`
`= [(costhetacosphi - sintheta sinphi, -sinthetacosphi - costhetasinphi),(costhetasinphi + sinthetacosphi, -sinthetasinphi + costhetacosphi)]`
`= [(cos (theta + phi) - sin (theta + phi)), (sin (theta + phi) cos (theta + phi))]` ...(ii)
From (i) and (ii), we get
AB = BA
APPEARS IN
संबंधित प्रश्न
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
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 = `[(-2, 3, -1),(-1, 2, -1),(-6, 9, -4)], "B" = [(1, 3, -1),(2, 2, -1),(3, 0, -1)]`
If A = `[(4, 8),(-2, -4)]`, prove that A2 = 0
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(4, -2),(2, 3)], "B" = [(-1, 1),(3, -2)] and "C" = [(4, 1),(2, -1)]`
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
A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A2 = B.
Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`
Find k, if A= `[(3, -2),(4, -2)]` and if A2 = kA – 2I
Find x, if `[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0
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")]`
Jay and Ram are two friends in a class. Jay wanted to buy 4 pens and 8 notebooks, Ram wanted to buy 5 pens and 12 notebooks. Both of them went to a shop. The price of a pen and a notebook which they have selected was Rs.6 and Rs.10. Using Matrix multiplication, find the amount required from each one of them
Select the correct option from the given alternatives:
If `[(5, 7),(x, 1),(2, 6)] - [(1, 2),(-3, 5),(2, y)] = [(4, 5),(4, -4),(0, 4)]` then __________
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 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)
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 = `[(2, -2, -4),(-1, 3, 4),(1, -2, -3)]` show that A2 = A
Answer the following question:
If A = `[(3, -5),(-4, 2)]`, show that A2 – 5A – 14I = 0
Answer the following question:
If A = `[(2, -1),(-1, 2)]`, show that A2 – 4A + 3I = 0
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
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)]`
