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Linear Algebra 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 1.3.1
Multiply by .
Step 1.3.2
Multiply by .
Step 1.3.3
Multiply by .
Step 2
Write as a linear system of equations.
Step 3
Step 3.1
Replace all occurrences of with in each equation.
Step 3.1.1
Replace all occurrences of in with .
Step 3.1.2
Simplify the left side.
Step 3.1.2.1
Simplify .
Step 3.1.2.1.1
Remove parentheses.
Step 3.1.2.1.2
Add and .
Step 3.1.3
Replace all occurrences of in with .
Step 3.1.4
Simplify the left side.
Step 3.1.4.1
Simplify .
Step 3.1.4.1.1
Remove parentheses.
Step 3.1.4.1.2
Add and .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Replace all occurrences of with in each equation.
Step 3.3.1
Replace all occurrences of in with .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Combine the opposite terms in .
Step 3.3.2.1.1
Add and .
Step 3.3.2.1.2
Add and .
Step 3.4
Since is not true, there is no solution.