Find α and β that solve the vector equation
α [2 1] + β [1 3] = [5 0] (These are columns)
Solution:
Use definition CVA and definition CVSM to obtain a vector equation that we can use to make a system of equations.
[5 0] = α [2 1] + β [1 3] = [2α + β α + 3β]
By using definition CVE we can use the vector equation made above to create a system of equations.
2α + β = 5 α + 3β = 0
Solve the system of equations using row reduction.
[2 1 5 -> [1 0 3 1 3 0] 0 1 -1]
The steps for row reduction are 1/2 * row 1, (-1 * row 1) + row 2 and move answer to row 2, 2/5 * row 2, (-1/2 * row 2) + row 1 and move answer to row 1.
There is only one solution α = 3 and β = -1.