Finding Inverse of Matrix & Solving AB=C: Urgent Help Needed

[Rizzamabob]

Ok, i missed the class on finding the inverse of a matrix, and i only have a little bit of an idea on exactly what row operations i can do, when i try to make the matrix = its identity.

Another question I am stuck on.
Q.

I have 2 , 3 X 3 matrixs B and C respectivly.
The question is find A if AB=C, and i know B and C
Now, i know i cannot divide matrix's, and I am stuck as to what way i should travel to find the matrix A.
Thanks guys ! :shy:

 

[TD]

$$AB = C \Leftrightarrow ABB^{ - 1} = CB^{ - 1} \Leftrightarrow A = CB^{ - 1}$$

You only have to find the inverse of B.

 

[tacman]

Hi there,

Finding the inverse of a matrix can be a bit tricky, but with practice, it can become easier. The first step is to determine if the matrix is invertible. A matrix is invertible if its determinant is not equal to 0. If the determinant is 0, then the matrix does not have an inverse.

To find the inverse, you can use the Gauss-Jordan elimination method. Start by writing the given matrix and an identity matrix next to it. Then, use row operations such as multiplying a row by a constant, adding rows, or swapping rows to transform the given matrix into the identity matrix. The steps you take on the given matrix must also be taken on the identity matrix. Once the given matrix is transformed into the identity matrix, the identity matrix will become the inverse of the given matrix.

For your second question, finding A when AB=C, you can use the inverse matrix method. Multiply both sides by the inverse of B, which would be B^-1. This will give you A = B^-1 * C. So, in order to find A, you will need to find the inverse of B, which can be done using the method mentioned above.

I hope this helps! Don't worry if you missed the class, with practice, you will become more comfortable with finding the inverse of a matrix and solving equations involving matrices. Good luck!