Identify the two important questions in linear algebra about

Identify the two important questions in linear algebra about a solution to systems of linear equations. Explain how they are answered in the case of invertible matrices. Justify your answer!

Solution

writing the equations in form ax+by+cz=d

writing all the equations in matrix form AX=B

We can call the matrices \"A\", \"X\" and \"B\" and the equation becomes:

AX = B

Where

Then (as shown on the Inverse of a Matrix page) the solution is this:

X = A^-1B

This says that we can find the values of x, y and z (the X matrix) by multiplying the inverse of the A matrix by the B matrix.

solution exit when inverse of A is there. i.e matrix is invertible..