Linear Algebra Examples

Write as a Vector Equality 4ax-3y=7 , -x-by=8
,
Step 1
Write the system of equations in matrix form.
Step 2
Find the reduced row echelon form.
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Step 2.1
Rewrite as .
Step 2.2
Multiply each element of by to make the entry at a .
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Step 2.2.1
Multiply each element of by to make the entry at a .
Step 2.2.2
Simplify .
Step 2.3
Multiply each element of by to make the entry at a .
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Step 2.3.1
Multiply each element of by to make the entry at a .
Step 2.3.2
Simplify .
Step 3
Use the result matrix to declare the final solutions to the system of equations.
Step 4
Solve the equation for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Add to both sides of the equation.
Step 4.2.2
Add to both sides of the equation.
Step 5
Solve the equation for .
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Step 5.1
Add to both sides of the equation.
Step 5.2
Move all terms not containing to the right side of the equation.
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Subtract from both sides of the equation.
Step 6
The solution is the set of ordered pairs that makes the system true.
Step 7
Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.