Advertisements
Advertisements
प्रश्न
If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33.
उत्तर
We have,
A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`
a31 = 2, a32 = 4, a33 = 7
A31 = `|(2, 3),(1, 5)|` = 10 - 3 = 7
A32 = `- |(1, 3),(1, 5)|` = - (5 - 3) = - 2
A33 = `|(1, 2),(1, 1)|` = 1 - 2 = - 1
∴ a31A31 + a32A32 + a33A33
= 2(7) + 4(-2) + 7(-1)
= 14 - 8 - 7
= - 1
APPEARS IN
संबंधित प्रश्न
If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.
Find the matrix of the co-factor for the following matrix.
`[(1, 0, 2),(-2, 1, 3),(0, 3, -5)]`
Find the inverse of the following matrix.
`[(2, -3),(-1, 2)]`
Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by the adjoint method.
Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.
Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`
Fill in the blank :
If A = [aij]2x3 and B = [bij]mx1 and AB is defined, then m = _______
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
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 :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
If A(α) = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]` then prove that A2(α) = A(2α)
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
Solve by matrix inversion method:
2x – z = 0; 5x + y = 4; y + 3z = 5
If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
If A = `[(2, 2),(4, 5)]` and A–1 = λ(adj(A)), then λ = ______ .
If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A11, A11, A13 are co-factors of a11, a12, a13 respectively, then the value of a11A11 + a12A12 + a13A13 = ______.
If A–1 = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = ______.
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 ______.
If A = `[(-i, 0),(0, i)]`, then ATA is equal to
Find the cofactors of the elements of the matrix
`[(-1, 2),(-3, 4)]`
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.
If A = `[(cos α, sin α),(-sin α, cos α)]`, then find α satisfying `0 < α < π/2`, when A + AT = `sqrt(2) l_2` where AT is transpose of A.
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
