Question 825491
(First of all, algebra.com uses large parentheses, ( and ), around matrices instead of the more common large brackets, [ and ]. Keep this in mind as we go through the problem.)<br>
The fractions you got are not by themselves a sign of an error. The problems you are experiencing are due to the fact that you are misunderstanding the equation. It is <u>not</u>
{{{(4x+3)*(matrix(2, 2, 3, 2, 1, -2)) = (matrix(2, 2, 10, 8, 5, -2))}}}
Instead it is:
{{{4x+3*(matrix(2, 2, 3, 2, 1, -2)) = (matrix(2, 2, 10, 8, 5, -2))}}}
The important differences are:<ul><li>The first matrix is only multiplied by 3, not 4x+3.</li><li>The "x" is a matrix, not a number.</li></ul>Now let's solve for the matrix "x". Multiplying the first matrix by 3 we get:
{{{4x+(matrix(2, 2, 9, 6, 3, -6)) = (matrix(2, 2, 10, 8, 5, -2))}}}
Subtracting the matrix on the left from both sides we get:
{{{4x = (matrix(2, 2, 10, 8, 5, -2))-(matrix(2, 2, 9, 6, 3, -6)))}}}
which simplifies to:
{{{4x = (matrix(2, 2, 1, 2, 2, 4))}}}
Multiplying both sides by 1/4:
{{{x = (1/4)*(matrix(2, 2, 1, 2, 2, 4))}}}
which simplifies to:
{{{x = (matrix(2, 2, 1/4, 1/2, 1/2, 1))}}}
This is the solution.