HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If A = `[(8, 4),(10, 5)], "B" = [(5, -4),(10, -8)]` show that (A + B)² = A² + AB + B² 

If A = `[(3, 4),(-4, 3)] and "B" = [(2, 1),(-1, 2)]`, show that (A + B)(A – B) = A² – B² 

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 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")]`

If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that `"A"^2=[(cos2alpha, sin2alpha),(-sin2alpha, cos2alpha)]`

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

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 `[("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)

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 A_α = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that A_α . A_β = A_α+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 = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A² = I