Advertisements
Advertisements
प्रश्न
Check whether the following matrix is invertible or not:
`((2,3),(10,15))`
उत्तर
Let A = `((2,3),(10,15))`
Then, |A| = `|(2,3),(10,15)| = 30 - 30 = 0`
∴ A is a singular matrix.
Hence, A-1 does not exist.
APPEARS IN
संबंधित प्रश्न
Apply the given elementary transformation of the following matrix.
A = `[(1,0),(-1,3)]`, R1↔ R2
Apply the given elementary transformation of the following matrix.
A = `[(1,2,-1),(0,1,3)]`, 2C2
B = `[(1,0,2),(2,4,5)]`, −3R1
Find the addition of the two new matrices.
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.
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.
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:
`(("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))`
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)]`
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 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"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|`
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
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)]`
If A = `[(1, 2, -1),(3, -2, 5)]`, apply R1 ↔ R2 and then C1 → C1 + 2C3 on A
If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)−1
If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.
