Advertisements
Advertisements
प्रश्न
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
उत्तर
Let A = `[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
Then, |A| = `|(1, 2, 3),(2, 4, 5),(2, 4, 6)|`
= 1(24 – 20) – 2(12 – 10) + 3(8 – 8)
= 4 – 4 + 0
= 0
∴ A is a singular matrix.
∴ A is not invertible.
APPEARS IN
संबंधित प्रश्न
Find the matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I
Find the inverse of the following matrix by the adjoint method.
`[(-1,5),(-3,2)]`
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
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 = `[(1,2),(3,4)]`, and A (adj A) = kI, then the value of k is
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha, - "sin"alpha,0),("sin"alpha,"cos"alpha,0),(0,0,1)]` where α ∈ R, then [F(α)]-1 is
Choose the correct answer from the given alternatives in the following question:
The inverse of A = `[(0,1,0),(1,0,0),(0,0,1)]` is
Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`
Choose the correct alternative.
If a 3 x 3 matrix B has it inverse equal to B, thenB2 = _______
Fill in the blank :
(AT)T = _______
Fill in the blank :
If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
If the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α
If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)
If A = `[(0, 4, 3),(1, -3, -3),(-1, 4, 4)]`, then find A2 and hence find A−1
If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`, then verify that (AB)-1 = B-1A-1
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.
If A = `((-1,2),(1,-4))` then A(adj A) is
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.
If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A−1 = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.
If A is non-singular matrix and (A + l)(A - l) = 0 then A + A-1 = ______.
If A and Bare square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| = ______.
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A-1 is ______.
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
If A = `[(2, -3, 3),(2, 2, 3),(3, "p", 2)]` and A–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.
A–1 exists if |A| = 0.
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.