SOLUTION: Solve the following linear system using the INVERSE OF THE COEFFICIENT MATRIX. {{{system(x+2y=1,4x+5y=13)}}}

Abbreviate the above system by the AX=B form:



Now we need to find the inverse of the coefficient matrix



To find the inverse of a 2x2 matrix:

1. Interchange the upper left and lower right elements:



2. Multiply the upper right and lower left elements by -1:



3. Find the determinant of this matrix:



4. Divide every element of  by this value:



5. Simplify



That is the inverse of the coefficient matrix.

Left-multiply both sides of the matrix
equation:



by the inverse of the coefficient matrix:



Since matrix multiplication is associative, we move
the parentheses:



Now we multiply the two matrices on the far
left and the far right:



Simplify:







Multiply the matrices on the left:

 

Simplify:

 

So the solution is 

, 

Edwin