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Math 1050  Exam 3 Review
1. Solve the following system of equations in the manner indicated.
(a) By the Method of Substitution
(b) By elimination
(c) By Gaussian elimination (matrices)
(d) By GaussJordan elimination (matrices)
2. Graph each system of linear equations . How many
solutions does each system have? Label
and scale your axes.
3. At the movie theater, a bag of popcorn costs $5.00 and
a soda costs $3.00. If Darci buys
a total of 8 items and spends a total of $30.00 on just popcorn and soda, how
many bags
of popcorn and how many sodas does she buy?
4. Solve the systems of equations using any convenient method .
5. Find the equation of the parabola y = ax^2+bx+c that
passes through the points (−1, 2),
(1, 6) and (2, 17).
6. Find the partial fraction decomposition of the following.
7. Write the coefficient matrix and the augmented matrix of the following system.
8. Put the following matrix in rowechelon form and reduced row echelon form.
9. Perform the matrix operations given
(a) A + B
(b) 4B − A
(c) AB
(d) BA
10. If A is a 3×6 matrix and B is a 6×2 matrix, what dimensions does the product AB have?
11. Solve the matrix equation for X, where
12. Find the inverse of the matrix if it exists. Check your results.
13. (a) Find the inverse of the matrix
(b) Use your answer from part (a) to solve the following system .
14. Evaluate the determinant of the matrix.
(b)
i. Use cofactor expansion
ii. Use the alternative method
15. Use Cramer’s Rule to solve the system of equations.
16. Find the area of the triangle with vertices (0,−2), (2, 0) and (−1, 1).
17. Use a determinant to find whether the following points are collinear: (−1, 3), (0, 5), (1, 7).
18. Decode the following by using the inverse of
Recall that
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