# Name: ________________________________ Period: _______ – 10.4

```Name: ________________________________ Period: _______
GPS: Guided Problem Set 10.1 – 10.4
You must show ALL your work to receive full credit. Ask me to clarify if you have questions.
1. Solve for x.
8 x
 32
2 5
 3 3
0
2. . Let A  
and B  

2 5
 1
4
. Find 3A + B.
6 
1. ___________________ (+1)
2. ___________________ (+1)
  1 2  5
  5  3  7 
   1 2  6
3. Perform the matrix multiplication. 

 6  2 8    3  4  1


4. Solve the system using algebraic substitution or elimination.
3x  3 y  1
8
4x  y 
3
3. ___________________ (+1)
4. ___________________ (+1)
5. Solve by Cramer's Rule the following system of linear equations. Show ALL intermediate steps and the
complete reasoning required to support your chosen solution method.
x  2 y  z  3
2 x  4 y  z  7
 2 x  2 y  3z  4
5. (x,y,z) = ___________(+10)
6. Determine the inverse of the given matrix. In the table below, clearly state the row operation(s), show all
arithmetic work, and state the resultant augmented matrix that results after the operation(s). Show ALL steps
needed to produce the row echelon form. Write the inverse matrix in the space provided.(+10)
3 3 1
A  1 2 1
2  1 1
Row Operation(s)
A 1
Arithmetic Work














Resulting Matrix
```