HSC Science (Electronics) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If A = `[(1, 2),(3, 5)]` B = `[(0, 4),(2, -1)]`, show that AB ≠ BA, but |AB| = IAl·IBI

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

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If `[(5, 7),(x, 1),(2, 6)] - [(1, 2),(-3, 5),(2, y)] = [(4, 5),(4, -4),(0, 4)]` then __________

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If A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______

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If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______

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If A = `[(-2, 1),(0, 3)]` and f(x) = 2x² – 3x, then f(A) = ………

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If f(α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(– α)

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If f (α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(–α) + f(α)

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If A_α = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that A_α . A_β = A_α+β 

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If A = `[(2, -2, -4),(-1, 3, 4),(1, -2, -3)]` show that A² = A

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If A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A² = I

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If A = `[(3, -5),(-4, 2)]`, show that A² – 5A – 14I = 0

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If A = `[(2, -1),(-1, 2)]`, show that A² – 4A + 3I = 0

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if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A² – B² , find x and y

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If A = `[(0, 1),(1, 0)]` and B = `[(0, -1),(1, 0)]` show that (A + B)(A – B) ≠ A² – B² 

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If A = `[(2, -1),(3, -2)]`, find A³  

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Find x, y if, `[(0, -1, 4)]{2[(4, 5),(3, 6),(2, -1)] + 3[(4, 3),(1, 4),(0, -1)]} = [(x, y)]`

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Find x, y if, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`

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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)]`

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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)]`