Advertisements
Advertisements
प्रश्न
Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`
उत्तर
Let A = `[(2, -3),(3, 5)]`
Here,
a11 = 2
∴ M11 = 5 and A11 = (– 1)1+1 (5) = 5
a12 = – 3
∴ M12 = 3 and A12 = (– 1)1+2 (3) = – 3
a21 = 3
∴ M21 = – 3 and A21 = (– 1)2+1 (– 3) = 3
a22 = 5
∴ M22 = 2 and A22 = (– 1)2+2 (2) = 2
∴ The matrix of the co-factors is
[Aij]2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)] = [(5, -3),(3, 2)]`
Now, adj A = `["A"_"ij"]_(2xx2)^"T" = [(5, 3),(-3, 2)]`.
APPEARS IN
संबंधित प्रश्न
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation :
`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`
Using properties of determinants, prove that :
`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`
The cost of 2 books, 6 notebooks and 3 pens is Rs 40. The cost of 3 books, 4 notebooks and 2 pens is Rs 35, while the cost of 5 books, 7 notebooks and 4 pens is Rs 61. Using this information and matrix method, find the cost of 1 book, 1 notebook and 1 pen separately.
2x − y = 5
4x − 2y = 7
Find the cofactor matrix, of the following matrices: `[(5, 8, 7),(-1, -2, 1),(-2, 1, 1)]`
Choose the correct alternative.
If A = `[(2, 5),(1, 3)]`, then A–1 = _______
Choose the correct alternative:
If A = `[(1, 2),(2, -1)]`, then adj (A) = ______
For which values of xis the matrix
`[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` non-invertible?
If `overlinea = hati + hatj + hatk, overlinea . overlineb = 1` and `overlinea xx overlineb = hatj - hatk,` then `overlineb` = ______
In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: elements a23, a31, a12
Find non-zero values of x satisfying the matrix equation:
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
On using elementary row operation R1 → R1 – 3R2 in the following matrix equation: `[(4, 2),(3, 3)] = [(1, 2),(0, 3)] [(2, 0),(1, 1)]`, we have: ______.
In applying one or more row operations while finding A–1 by elementary row operations, we obtain all zeros in one or more, then A–1 ______.
A matrix denotes a number.
If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.
If A = `[(2, 3, -1),(1, 4, 2)]` and B = `[(2, 3),(4, 5),(2, 1)]`, then AB and BA are defined and equal.
`abs((1,1,1),("e",0,sqrt2),(2,2,2))` is equal to ____________.
If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then" x = 1 "and" y = -1`
