Linear Algebra Examples

Solve the Matrix Equation [[1,7],[4,2]]*[[x],[y]]=[[30],[-10]]
Step 1
Multiply .
Tap for more steps...
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
Solve the system of equations.
Tap for more steps...
Step 3.1
Subtract from both sides of the equation.
Step 3.2
Replace all occurrences of with in each equation.
Tap for more steps...
Step 3.2.1
Replace all occurrences of in with .
Step 3.2.2
Simplify the left side.
Tap for more steps...
Step 3.2.2.1
Simplify .
Tap for more steps...
Step 3.2.2.1.1
Simplify each term.
Tap for more steps...
Step 3.2.2.1.1.1
Apply the distributive property.
Step 3.2.2.1.1.2
Multiply by .
Step 3.2.2.1.1.3
Multiply by .
Step 3.2.2.1.2
Add and .
Step 3.3
Solve for in .
Tap for more steps...
Step 3.3.1
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.3.1.1
Subtract from both sides of the equation.
Step 3.3.1.2
Subtract from .
Step 3.3.2
Divide each term in by and simplify.
Tap for more steps...
Step 3.3.2.1
Divide each term in by .
Step 3.3.2.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.2.1.1
Cancel the common factor.
Step 3.3.2.2.1.2
Divide by .
Step 3.3.2.3
Simplify the right side.
Tap for more steps...
Step 3.3.2.3.1
Divide by .
Step 3.4
Replace all occurrences of with in each equation.
Tap for more steps...
Step 3.4.1
Replace all occurrences of in with .
Step 3.4.2
Simplify the right side.
Tap for more steps...
Step 3.4.2.1
Simplify .
Tap for more steps...
Step 3.4.2.1.1
Multiply by .
Step 3.4.2.1.2
Subtract from .
Step 3.5
List all of the solutions.