Advertisements
Advertisements
Question
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
Solution
A=`[[1,2],[1,3]]`
|A|=3-2
=1≠ 0
∴`A_1` exists
We have `A=A^-1=I`
`[[1,2],[1,3]]A^1`=`[[1,0],[0,1]]`
Applying` R_2→R_2-R_1`
`[[1 ,2],[0,1]]A^1=[[1,0],[-1, 1]]`
Applying `R_1→R_1-2R_2`
`[[1,0],[0,1]]A^1=[[3,-2],[-1 ,1]]`
Hence `A^-1=[[3,-2],[-1,1]]`
APPEARS IN
RELATED QUESTIONS
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
State, whether the following statement is true or false. If false, give a reason.
Transpose of a 2 × 1 matrix is a 2 × 1 matrix.
If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A – B)2 = A2 – 2A . B + B2
Find cofactors of the elements of the matrix A = `[[-1,2],[-3,4]]`
Solve the following system of linear equation using matrix method:
`1/x + 1/y +1/z = 9`
`2/x + 5/y+7/z = 52`
`2/x+1/y-1/z=0`
Classify the following matrix :
`|(1 , 1),(0,9)|`
If A = `|(1,9,4),(5 , 0 , 3)|` find A'
Evaluate the following :
`|(2 , 3),(-4 , 0)| |(3 , -2),(-1 , 4)|`
If A = `[(2, 3), (1, 2)], B = [(1, 0),(3, 1)]`, Find (AB)-1
If A = `[(1,2), (1,3)]`, find A2 - 3A
Find the adjoint of the matrix `"A" = [(2,-3),(3,5)]`
Solve the following minimal assignment problem :
| Machines | Jobs | ||
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
[2 3 – 7]
Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" - "j")^2)/(5 - "i")`
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = i – 3j
If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.
