Find the inverse of the matrix A = [2 5; 1 3].a.[3 1; -5 2]b.[3 -5; -1 2]c.[2 -5; 1 3]d.[3 -1; -5 2]
Question
Find the inverse of the matrix A = [2 5; 1 3].a.[3 1; -5 2]b.[3 -5; -1 2]c.[2 -5; 1 3]d.[3 -1; -5 2]
Solution
To find the inverse of a 2x2 matrix A = [a b; c d], we use the formula:
A^(-1) = 1/(ad-bc) * [d -b; -c a]
Given the matrix A = [2 5; 1 3], let's calculate its inverse:
First, calculate the determinant (ad-bc): (23) - (51) = 6 - 5 = 1
Then, swap the positions of a and d, and change the signs of b and c:
[d -b; -c a] = [3 -5; -1 2]
Finally, multiply by 1/(ad-bc):
A^(-1) = 1/1 * [3 -5; -1 2] = [3 -5; -1 2]
So, the inverse of the matrix A = [2 5; 1 3] is [3 -5; -1 2], which corresponds to option (b).
Similar Questions
Find the inverse of matrix B = [[2, 1], [5, 3]]
If the matrix is invertible, find its inverse:A = .−1 2 −32 1 04 −2 5
What is the inverse of a 2x2 matrix A = [[a, b], [c, d]]?a.1/(ad-bc) * [[a, b], [c, d]]b.1/(ad+bc) * [[a, -b], [-c, d]]c.1/(ad+bc) * [[d, b], [c, a]]d.1/(ad-bc) * [[d, -b], [-c, a]]
compute the inverse B of the matrix, A=(13 11 9 12, 11 6 3 10, 17 8 10 9, 33 6 1 2)
The inverse of the function {(1,3),(2,1),(4,5)} isA.{(3,1),(2,1)(4,5)}{(3,1),(2,1)(4,5)}B.{(1,3),(2,1)(5,4)}{(1,3),(2,1)(5,4)}C.{(3,1),(1,2)(5,4)}{(3,1),(1,2)(5,4)}D.{(3,1),(2,1)(5,4)}{(3,1),(2,1)(5,4)}
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.