Advertisements
Advertisements
Question
If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33.
Solution
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
RELATED QUESTIONS
Find the inverse of the following matrix by elementary row transformations if it exists.
`A = [(1, 2, -2), (0, -2, 1), (-1, 3, 0)]`
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.
`[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`
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 matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
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.
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
(AT)T = _______
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(1, -1, 1),(2, 1, -3),(1, 1, 1)]`, 10B = `[(4, 2,2),(-5, 0, ∞),(1, -2, 3)]` and B is the inverse of matrix A, then α = ______
If A = `[(3, 1),(5, 2)]`, and AB = BA = I, then find the matrix B
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
Solve by matrix inversion method:
2x – z = 0; 5x + y = 4; y + 3z = 5
The prices of three commodities A, B, and C are ₹ x, y, and z per unit respectively. P purchases 4 units of C and sells 3 units of A and 5 units of B. Q purchases 3 units of B and sells 2 units of A and 1 unit of C. R purchases 1 unit of A and sells 4 units of B and 6 units of C. In the process P, Q and R earn ₹ 6,000, ₹ 5,000 and ₹ 13,000 respectively. By using the matrix inversion method, find the prices per unit of A, B, and C.
The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
Which of the following matrix has no inverse
If A is an invertible matrix of order 2 then det (A-1) be equal
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B-1A-1 = ?
If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______
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 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.
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 A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I
Find the inverse of the matrix `[(1, 1, 1),(1, 2, 3),(3, 2, 2)]` by elementary column transformation.
