Matrix Equations Systems Test – Precalculus Math (Printable PDF)

Question 1 From Equations to Matrices (3 points)

Consider the system 3x − 5y = −4 and 2x + y = 7.

1. Write the system as AX = B and state A, X and B. (1 point)
2. Find det A. (1 point)
3. Does the system have a unique solution? Explain. (1 point)

Question 2 Solve Using an Inverse (3 points)

The figure shows the graph of 3x + 2y = 4 and 7x + 4y = 6. Solve the system using an inverse matrix.

Question 3 Type of Solution Set (2 points)

Consider 4x − 6y = 10 and −6x + 9y = −15.

1. Find the determinant of the coefficient matrix. (1 point)
2. Describe the solution set and explain. (1 point)

Question 4 Images of Points (2 points)

The matrix M has rows (2, −1) and (0, 3). Find the images of (4, −2) and (−1, 5).

Question 5 A Triangle Transformed (3 points)

The triangle in the figure is transformed by the matrix with rows (2, 0) and (1, 1).

1. Find the images of the three vertices. (1 point)
2. Find the determinant and the area of the image triangle. (2 points)

Question 6 Matrices from Descriptions (2 points)

(a) The matrix with rows (1, 0) and (0, −1) reflects points in the x-axis. Find the image of (−3, 7). (1 point)

(b) Write the matrix of the 90° clockwise rotation by finding where (1, 0) and (0, 1) go. (1 point)

Question 7 Snack Bar Prices (3 points)

On Monday a snack bar sold 6 bagels and 2 juices for $18.00. On Tuesday it sold 5 bagels and 3 juices for $17.00.

1. Write a matrix equation for the prices b and j. (1 point)
2. Solve it with an inverse matrix, and state the price of each item. (2 points)

Question 8 Singular System (2 points)

For the system 3x + ky = 9 and 2x + 4y = 5, find the value of k that gives no unique solution. Then decide whether the system has no solution or infinitely many for that k.