Augmented Matrix Exit Ticket
Algebra 2 Linear Systems & Matrices
Augmented Matrix Exit Ticket
Score _____ / 10
Name:
Date:
Period:
1
Representing Systems as Augmented Matrices
[3 pts]
Write the augmented matrix that represents the 3-variable linear system below. Pay close attention to missing variables and constant terms.
System of Equations
\(2x - 3y + z = 9\)
\(4x + 5z = -2\)
\(-x + y = 6\)
Augmented Matrix \([A \mid B]\):
2
Interpreting Solution Types
[4 pts]
Classify each reduced augmented matrix by its solution type: One Unique Solution, No Solution (Inconsistent), or Infinitely Many Solutions (Dependent). Then provide your reasoning.
Matrix A: Variables: \(x, y, z\)
\[\left[\begin{array}{ccc|c} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 0 & 7 \end{array}\right]\]
Type:
Explain the bottom row:
Matrix B: Variables: \(x, y, z\)
\[\left[\begin{array}{ccc|c} 1 & 0 & 2 & 3 \\ 0 & 1 & -1 & 5 \\ 0 & 0 & 0 & 0 \end{array}\right]\]
Type:
Explain the bottom row:
3
Performing a Row Operation
[3 pts]
Given the matrix below, perform the row operation: \(-3R_1 + R_2 \to R_2\). Show scratch work for each entry and write the resulting new matrix.
Current Matrix
\[\left[\begin{array}{cc|c} 1 & 4 & 5 \\ 3 & -2 & 1 \end{array}\right]\]
Scratch Work for \(R_2\):
Updated Matrix:
Confidence Level:
1 (Unclear) 2 (Getting There) 3 (Confident)
One lingering question:
