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Math 1050 - Exam 3 Review
- Solve the following system of equations in the manner indicated. { x + 2y = 6 3 x − y = 9 (a) By the Method of Substitution (b) By elimination (c) By Gaussian elimination (matrices) (d) By Gauss-Jordan elimination (matrices)
- Graph each system of linear equations. How many solutions does each system have? Label and scale your axes. (a)
2 x + 2y = 10 9 x − 3 y = 3 (b)
x − 2 y = 2 2 x − 4 y = − 16
- 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?
- Solve the systems of equations using any convenient method.
(a)
x + 2y − z = 1 y + 6z = − 2 z = 4 (b)
x − 2 y = 4 4 x − 8 y = 6
(c)
x + 2y + 3z = 7 4 x − y − 5 z = − 3 3 x + 2y − z = 6 (d)
x^2 + y^2 = 17 3 x + 5y = 7 (e)
2 x + 4y − 3 z = − 1 − 3 x − 4 y + 2z = 5
(f)
x + 2y = 0 x + y = 6 3 x − 2 y = 8
- Find the equation of the parabola y = ax^2 + bx + c that passes through the points (− 1 , 2), (1, 6) and (2, 17).
- Find the partial fraction decomposition of the following. (a) (^) x (^2 2) + 3x^ + 3x + 2 (b) (^) (x − 1)x^2 −(^ x^52 + 9)
(c) x
(^3) + x (^2) + x + 3 x^2 + 5x + 6
- Write the coefficient matrix and the augmented matrix of the following system.
− 5 x + 7y + 9z = − 11 16 x − 8 y + 4z = − 2 3 x + 6y − 9 z = 12
- Put the following matrix in row-echelon form and reduced row-echelon form.
- Perform the matrix operations given
A =
(^) and B =
(a) A + B (b) 4 B − A (c) AB (d) BA
- If A is a 3 × 6 matrix and B is a 6 × 2 matrix, what dimensions does the product AB have?
- Solve the matrix equation 13 X − A = B for X, where A =
[ 1 − 4
]
and B =
[ 2
]
- Find the inverse of the matrix if it exists. Check your results.
(a)
[ 7 4
]
(b)
- (a) Find the inverse of the matrix
[ 3 5
]
