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
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 matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
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),(1,-1))`
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____
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
Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.
Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______
If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method
If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
Find the inverse of the following matrix:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A-1 = `[(1,0,3),(2,1,-1),(1,-1,1)]` then, find A.
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
Solve by matrix inversion method:
2x – z = 0; 5x + y = 4; y + 3z = 5
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.
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-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 = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.
If A and Bare square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| = ______.
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If AB = I and B = AT, then _______.
If `A = [[-3,1],[-4,3]]` and A-1 = αA, then α = ______.
If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0
