I have TWO Matrices Problems for you. Help??

Question

Okay, so i have two matrices problems that I need help in solving and wondering what the answer would be:

First Matrix:
Evaluate A^(-1)
Given: (this is a 2x2 matrix) A= [6,4,3,2]

Second Matrix:
Evaluate B^(-1)
Given: (this is a 2x2 matrix) B = [2,1,5,3]

Thank you for your help to anyone who submitted solutions! :)

Answer 1

The first thing you should note is that they are asking you to find the inverse of the matrixes. To do that you should take the matrix that you are given and attach an identity matrix to it on the right. So:
A = 6 4 1 0
3 2 0 1
B = 2 1 1 0
5 3 0 1

So now do row reduction. Essentially, add and subtract the rows to each other to arrive at the identity matrix being on the left. You may have to multiply the rows before you add. This is ok just make sure when you add or multiply or do any other operation that you apply it to all elements in that row.

If you try this with A you will find out that it is singular. Notice that the first and second rows are multiples of each other.

If you try this with B your resulting matrix is:
1 0 3 -1
0 1 -5 2

The right portion is the inverse of the matrix, so your answer would be

3 -1
-5 2
..

Answer 2

For 2X2 Matrix A with the elements
a11 a12 a21 a22 (first digit stands for the row 2nd for column) the the the elements of the inverse B = A⁻¹ are given by:
b11 = a22/detA
b12 = -a12/detA
b21 = -a21/detA
b22 = a11/detA
with detA = a11·a22 - a12·a21

The inverse Matrices are:

Matrix A
detA = 6·2 - 3·4 = 0
That means that matrix A is not invertible

Matrix B
detB = 2·3 - 5·1 = 1
B⁻¹ = [3, -1 , -5 , 2]

Answer 3

You should just do it! It's a 'plug and chug' operation.