3-2 Assignment Worksheet
Finite Math Matrices & Linear Systems
3-2 Assignment
Scalar Operations with Matrices
Name:
Date: Period:
Scalar Rule: Multiply every matrix entry by the scalar \(k\): \( k [a_{ij}] = [k \cdot a_{ij}] \)
Order of operations: multiply scalars before adding or subtracting.
A Part 1: Basic Scalar Multiplication
Simplify each scalar product completely.
- \( 2 \times 2 \)
\[ 3 \begin{bmatrix} 2 & -4 \\ 5 & 1 \end{bmatrix} \]
Answer Matrix:
- \( 2 \times 3 \)
\[ -2 \begin{bmatrix} 1 & 0 & -3 \\ 4 & -2 & 5 \end{bmatrix} \]
Answer Matrix:
- \( 3 \times 2 \)
\[ \frac{1}{2} \begin{bmatrix} 8 & -12 \\ -4 & 6 \\ 10 & 0 \end{bmatrix} \]
Answer Matrix:
- \( 3 \times 3 \)
\[ 4 \begin{bmatrix} -1 & 3 & 2 \\ 0 & -2 & 4 \\ 5 & 1 & -3 \end{bmatrix} \]
Answer Matrix:
B Part 2: Multi-Step Operations
Multiply by the scalar first, then add or subtract.
- Given \( A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 2 \\ -3 & 1 \end{bmatrix} \), find \( 2A + B \)
\( 2 \times 2 \)
Show intermediate step \( 2A \):
Final Matrix Answer:
Finite Math • 3-2 Assignment: Scalar Operations with Matrices Page 1 of 2
Finite Math
3-2 Assignment
Multi-Step Operations & Linear Combinations
Name:
- Given \( C = \begin{bmatrix} 4 & -2 & 1 \\ 0 & 3 & -5 \end{bmatrix} \) and \( D = \begin{bmatrix} 1 & 4 & -2 \\ 6 & -1 & 3 \end{bmatrix} \), find \( 3C - D \)
\( 2 \times 3 \)
Show intermediate work (scale \( C \), then subtract \( D \)):
Final Matrix Answer:
- Given \( P = \begin{bmatrix} 2 & 7 \\ -1 & 0 \\ 4 & -3 \end{bmatrix} \) and \( Q = \begin{bmatrix} -3 & 1 \\ 5 & 2 \\ 0 & -4 \end{bmatrix} \), find \( P + 4Q \)
\( 3 \times 2 \)
Show intermediate work (scale \( Q \), then add \( P \)):
Final Matrix Answer:
- Given \( A = \begin{bmatrix} 2 & -1 \\ 3 & 5 \end{bmatrix} \) and \( B = \begin{bmatrix} 4 & 0 \\ -2 & 1 \end{bmatrix} \), find \( 3A + 2B \)
\( 2 \times 2 \)
Show scaled matrices \( 3A \) and \( 2B \):
Final Matrix Answer:
- Given \( X = \begin{bmatrix} 1 & 0 & -2 \\ -3 & 2 & 1 \\ 4 & -1 & 0 \end{bmatrix} \) and \( Y = \begin{bmatrix} 0 & 3 & 1 \\ 2 & -1 & 4 \\ -2 & 0 & 5 \end{bmatrix} \), find \( -2X + 5Y \)
\( 3 \times 3 \)
Show scaled matrices \( -2X \) and \( 5Y \):
Final Matrix Answer:
Finite Math • 3-2 Assignment: Scalar Operations with Matrices Page 2 of 2
3-2 Assignment Answer Key
Finite Math Teacher Key & Solutions
3-2 Assignment Key
Scalar Operations with Matrices
9 Problems Total • 10 Pts Each
5 pts intermediate work, 5 pts final matrix
Grading Note: Check that the scalar is distributed to every element inside the matrix.
Check sign changes with negative scalars.
A Part 1: Basic Scalar Multiplication (Problems 1–4)
10 pts each
- \( 2 \times 2 \)
\( 3 \begin{bmatrix} 2 & -4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 3(2) & 3(-4) \\ 3(5) & 3(1) \end{bmatrix} \)
Correct Matrix
\[ \begin{bmatrix} 6 & -12 \\ 15 & 3 \end{bmatrix} \]
- \( 2 \times 3 \)
\( -2 \begin{bmatrix} 1 & 0 & -3 \\ 4 & -2 & 5 \end{bmatrix} = \begin{bmatrix} -2(1) & -2(0) & -2(-3) \\ -2(4) & -2(-2) & -2(5) \end{bmatrix} \)
Correct Matrix
\[ \begin{bmatrix} -2 & 0 & 6 \\ -8 & 4 & -10 \end{bmatrix} \]
- \( 3 \times 2 \)
\( \frac{1}{2} \begin{bmatrix} 8 & -12 \\ -4 & 6 \\ 10 & 0 \end{bmatrix} = \begin{bmatrix} 8/2 & -12/2 \\ -4/2 & 6/2 \\ 10/2 & 0/2 \end{bmatrix} \)
Correct Matrix
\[ \begin{bmatrix} 4 & -6 \\ -2 & 3 \\ 5 & 0 \end{bmatrix} \]
- \( 3 \times 3 \)
\( 4 \begin{bmatrix} -1 & 3 & 2 \\ 0 & -2 & 4 \\ 5 & 1 & -3 \end{bmatrix} \) Scale all 9 entries by 4
Correct Matrix
\[ \begin{bmatrix} -4 & 12 & 8 \\ 0 & -8 & 16 \\ 20 & 4 & -12 \end{bmatrix} \]
B Part 2: Multi-Step Operations (Problem 5)
10 pts
- Given \( A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 2 \\ -3 & 1 \end{bmatrix} \), find \( 2A + B \)
\( 2 \times 2 \)
Step 1 (Scale \(A\)): \( 2A = \begin{bmatrix} 6 & -2 \\ 4 & 8 \end{bmatrix} \)
Step 2 (Add \(B\)): \( \begin{bmatrix} 6+5 & -2+2 \\ 4+(-3) & 8+1 \end{bmatrix} \)
⚠️ Note: \( -2 + 2 = 0 \) in position \( (1,2) \).
Final Answer
\[ 2A + B = \begin{bmatrix} 11 & 0 \\ 1 & 9 \end{bmatrix} \]
Finite Math • 3-2 Assignment Answer Key Page 1 of 2
Finite Math
3-2 Assignment Solutions
Teacher Key • Problems 6–9
Linear Combinations
- Given \( C = \begin{bmatrix} 4 & -2 & 1 \\ 0 & 3 & -5 \end{bmatrix} \) and \( D = \begin{bmatrix} 1 & 4 & -2 \\ 6 & -1 & 3 \end{bmatrix} \), find \( 3C - D \)
