Linear Math

Sample Quiz 1

Given the following system of equations 2x1 − 3x2  1 x1  5x2  7

1. Write this system as a matrix equation. 2. Write this system as an augmented matrix. 3. Use row operations to put the augmented matrix in reduced echelon form and show which operations you did. 4. Is this system consistent and why? 5. Is the b vector in the span of the column vectors of matrix A, why or why not?

Given the following system of equations x1  2x2  2x3  9 x1  3x2 − 4x3  5

2x1  5x2 − 2x3  14 6. Write this system as a matrix equation. 7. Write this system as an augmented matrix. 8. Use row operations to put the augmented matrix in reduced echelon form and show which operations you did. 9. Is this system consistent and why? 10. Is the b vector in the span of the column vectors of matrix A, why or why not?

Given the following system of equations

You can do this question using Wolfram Alpha, Mathematica, MATLAB or any tool that you like or if you prefer by hand.

x1  3x2 − x3  2x4  −2 2x1  7x2  2x3 − x4  19 − 3x1 − 8x2  3x3  x4  −7 4x1  11x2 − 2x3 − 3x4  19

For example you could use in Wolfram Alpha rownreduce  1,3,−1,2,−2, 2,7,2,−1,19, −3,−8,3,1,−7, 4,11,−2,−3,19 

1. Is the b vector in the span of the column vectors of matrix A, why or why not?