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Finite Math Examples
Step 1
Step 1.1
Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is and the second matrix is .
Step 1.2
Multiply each row in the first matrix by each column in the second matrix.
Step 1.3
Simplify each element of the matrix by multiplying out all the expressions.
Step 2
Write as a linear system of equations.
Step 3
Step 3.1
Add to both sides of the equation.
Step 3.2
Replace all occurrences of with in each equation.
Step 3.2.1
Replace all occurrences of in with .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Simplify .
Step 3.2.2.1.1
Simplify each term.
Step 3.2.2.1.1.1
Apply the distributive property.
Step 3.2.2.1.1.2
Multiply by .
Step 3.2.2.1.2
Subtract from .
Step 3.3
Move all terms not containing to the right side of the equation.
Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Subtract from .
Step 3.4
Replace all occurrences of with in each equation.
Step 3.4.1
Replace all occurrences of in with .
Step 3.4.2
Simplify .
Step 3.4.2.1
Simplify the left side.
Step 3.4.2.1.1
Remove parentheses.
Step 3.4.2.2
Simplify the right side.
Step 3.4.2.2.1
Subtract from .
Step 3.5
List all of the solutions.