HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Apply the given elementary transformation of the following matrix.

A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R₃ and then C₃ + 2C₂

and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C₃ + 2C₂ and then 3R₃
What do you conclude?

Apply the given elementary transformation of the following matrix.

Use suitable transformation on `[(1,2),(3,4)]` to convert it into an upper triangular matrix.

Apply the given elementary transformation of the following matrix.

Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.

Apply the given elementary transformation of the following matrix.

Transform `[(1,-1,2),(2,1,3),(3,2,4)]` into an upper triangular matrix by suitable column transformations.

The total cost of 3 T.V. sets and 2 V.C.R.’s is ₹ 35,000. The shopkeeper wants a profit of ₹ 1000 per T.V. set and ₹ 500 per V.C.R. He sells 2 T.V. sets and 1 V.C.R. and gets the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. set and a V.C.R.

If A = `((1,0,0),(2,1,0),(3,3,1))`, then reduce it to I₃ by using column transformations.

If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I₃ by using row transformations.

Check whether the following matrix is invertible or not:

`[(1,0),(0,1)]`

Check whether the following matrix is invertible or not:

`((1,1),(1,1))`

Check whether the following matrix is invertible or not:

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

Check whether the following matrix is invertible or not:

`((2,3),(10,15))`

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:

`((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.