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

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.

Find the inverse of the following matrix (if they exist).

`[(1,3,-2),(-3,0,-5),(2,5,0)]`

Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(3,4)]` , adj A = `[(4,"a"),(-3,"b")]`, then the values of a and b are

Choose the correct answer from the given alternatives in the following question:

The inverse of `[(0,1),(1,0)]` is

Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is

The differential equation `y dy/dx + x = 0` represents family of ______.

Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is

The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.

If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A² 

If A = `[(-2, 4),(-1, 2)]` then find A² 

Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`

Find A⁻¹ using column transformations:

A = `[(5, 3),(3, -2)]`

Find A⁻¹ using column transformations:

A = `[(2, -3),(-1, 2)]`