HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Check whether the following matrix is invertible or not:

`[(cos theta, sin theta),(-sin theta, cos theta)]`

Check whether the following matrix is invertible or not:

`(("sec" theta , "tan" theta),("tan" theta,"sec" theta))`

Check whether the following matrix is invertible or not:

`((3,4,3),(1,1,0),(1,4,5))`

Check whether the following matrix is invertible or not:

`((1,2,3),(2,-1,3),(1,2,3))`

Check whether the following matrix is invertible or not:

`((1,2,3),(3,4,5),(4,6,8))`

If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A⁻¹ by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`

If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.

Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row transformations.

Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary column transformations.

If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, find AB and (AB)^-1 . Verify that (AB)^-1 = B^-1.A^-1.

If A = `[(4,5),(2,1)]`, show that `"A"^-1 = 1/6("A" - 5"I")`.

Find the matrix X such that AX = B, where A = `[(1,2),(-1,3)]` and B = `[(0,1),(2,4)]`

Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`

If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C

Find A^-1 by the adjoint method and by elementary transformations, if A = `[(1,2,3),(-1,1,2),(1,2,4)]`

Find the inverse of A = `[(1,0,1),(0,2,3),(1,2,1)]` by using elementary column transformations.

Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.

Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3)  "is"   "a"_11"A"_21 + "a"_12"A"_22 + "a"_13"A"_23 = 0` 

Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3)  "is"   "a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|` 

If A = `[(1,0,1),(0,2,3),(1,2,1)]` and B = `[(1,2,3),(1,1,5),(2,4,7)]`, then find a matrix X such that XA = B.