Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
पर्याय
0
5
10
25
उत्तर
5
Explanation:
A(adj A) = |A| I
A(adj A) = `[(5, 0),(0, 5)] = 5[(1, 0),(0, 1)]`
∴ |A| = 5.
APPEARS IN
संबंधित प्रश्न
The sum of three numbers is 6. If we multiply the third number by 3 and add it to the second number we get 11. By adding first and third numbers we get a number, which is double than the second number. Use this information and find a system of linear equations. Find these three numbers using matrices.
Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.
Find the inverse of the following matrix by the adjoint method.
`[(-1,5),(-3,2)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverse of the following matrix (if they exist):
`[(2,1),(7,4)]`
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______
Choose the correct answer from the given alternatives in the following question:
For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals
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.
Choose the correct alternative.
If AX = B, where A = `[(-1, 2),(2, -1)], "B" = [(1),(1)]`, then X = _______
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
If A = `[(3, -5),(2, 5)]`, then co-factor of a12 is _______
Fill in the blank :
(AT)T = _______
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
Check whether the following matrices are invertible or not:
`[(1, 0),(0, 1)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
The solution (x, y, z) of the equation `[(1, 0, 1),(-1, 1, 0),(0, -1, 1)] [(x),(y),(z)] = [(1),(1),(2)]` is (x, y, z) =
If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`
If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'
If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
Show that the matrices A = `[(2,2,1),(1,3,1),(1,2,2)]` and B = `[(4/5,(-2)/5,(-1)/5),((-1)/5,3/5,(-1)/5),((-1)/5,(-2)/5,4/5)]` are inverses of each other.
If A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`, then verify that (AB)-1 = B-1A-1
Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.
A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.
| Months | Sales in units | Commission | ||
| A | B | C | ||
| January | 9 | 10 | 2 | 800 |
| February | 15 | 5 | 4 | 900 |
| March | 6 | 10 | 3 | 850 |
Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
The inverse matrix of `((3,1),(5,2))` is
If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.
If A = `[(1,2),(3,-5)]`, then A-1 = ?
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
Choose the correct option:
If X, Y, Z are non zero real numbers, then the inverse of matrix A = `[(x, 0, 0),(0, y, 0),(0, 0, z)]`
If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
