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

In summary, to find the matrix A in the equation AB = C, you can use the formula A = CB^-1, where B is the inverse of B and C is the known matrix.
  • #1
Rizzamabob
21
0
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: :uhh:
 
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  • #2
[tex]AB = C \Leftrightarrow ABB^{ - 1} = CB^{ - 1} \Leftrightarrow A = CB^{ - 1}[/tex]

You only have to find the inverse of B.
 
  • #3


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!
 

1. What is an inverse matrix?

An inverse matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. In other words, it "undoes" the original matrix and returns it to its original state.

2. How do you find the inverse of a matrix?

The inverse of a matrix can be found by using the Gauss-Jordan elimination method or by using the adjugate method. The Gauss-Jordan elimination method involves performing elementary row operations on the original matrix until it is transformed into the identity matrix. The resulting matrix is the inverse of the original matrix. The adjugate method involves finding the adjugate matrix and dividing it by the determinant of the original matrix.

3. Can every matrix have an inverse?

No, not every matrix has an inverse. A matrix must be square (same number of rows and columns) and have a non-zero determinant in order to have an inverse. If the determinant is zero, the matrix is said to be singular and does not have an inverse.

4. What is the purpose of finding the inverse of a matrix?

The inverse of a matrix is useful in solving linear equations, as it allows us to solve for the unknown variables in the equation. It is also used in various applications such as computer graphics, cryptography, and engineering.

5. How is AB=C solved using the inverse of a matrix?

In order to solve AB=C using the inverse of a matrix, we first find the inverse of matrix A. Then, we multiply both sides of the equation by A^-1 to isolate matrix B on one side. This results in the equation B = A^-1 * C. We can then solve for B by multiplying A^-1 by C.

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