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Systems of Two Equations
Matrix Algebra
Row Operations
Partial Fractions
Miscellaneous
100
Solve by elimination. x-y=5 x+2y=2
What is (4,1)?
100
Determine the dimensions of this matrix. [3 4 5 6 8 9]
What is a 1x6 matrix?
100
Solve for the systems of equations: x+2y=1 4y-4=-2x
What is no solution?
100
Define partial fraction:
What is each fraction in the sum?
100
Determine the dimensions of the matrix: [2 ] [-1] [0 ]
What is a 3 x 1 matrix?
200
Solve by graphing the equations. y=x³-6x y=3x
What is (-3,-9), (0,0), (3,9)?
200
Add the two matrices: [2 3] + [1 6] [4 1] [9 2]
What is [3 9] ? [13 3]
200
Find the reduced row echelon form of the matrix: [1 0 2 ] [3 1 5 ] [1 -1 3]
What is [1 0 2] [0 1 -1] [0 0 0]
200
Find the partial fraction decomposition: 2 -------------- (x-5)(x-3)
What is 1 -1 ----- + ------ x-5 x-3
200
Solve the system: x+2y=1 4y-4=-2x
What is (1,2)?
300
Solve the systems by substitution. 2x-y=10 3x+2y=1
What is (3,-4)?
300
Subtract the two matrices. [2 3] - [1 -3] [-1 5] [-2 -4]
What is [1 6] ? [1 9]
300
Find the partial fraction decomposition: x+17 ---------------- 2x²+5x-3
What is -2 5 -------- + ----- x+3 2x-1
300
Find the partial fraction decomposition: 3x-2 ------------ x²-3x-4
What is 1 2 ---- + ---- x+1 x-4
400
At Philip's convenience store, the total cost of one medium and one large soda is $1.74. The large soda costs $0.16 more than the medium soda. Find the cost of each soda.
What is $0.79 for the medium soda and $0.95 for the large soda?
400
Find 2A - 3B. A= [-3 1] B= [4 0] [0 -1] [-2 1] [2 1] [-3 -1]
What is [-18 2] ? [6 -5] [13 5]
400
Write the system of equations corresponding to the augmented matrix: [3 2 -1] [-4 5 2]
What is 3x + 2y = -1 -4x +5y = 2
400
Find the partial fraction decomposition: x²+3x+2 --------------- (x^3-1)
What is 2 + -x ? ------ --------- x-1 x²+x+1
400
Find the equilibrium point for the demand and supply curves p=100 - x² p= 20 + 3x
What is (7.57, 42.71)?
500
Solve the system algebraically. x-3y=-2 2x-6y=4
What is no solution?
500
Verify that the matrices are inverses of each other. A= [2 1] B= [0.8 -0.2] [3 4] [-0.6 0.4]
What is yes
500
Solve the system of equations by finding the reduced row echelon form for the augmented matrix: x+2y-z=3 3x+7y-3z=12 -2x-4y+3z=-5
What is (-2, 3, 1)
500
Find the form of the partial fraction decomposition of: 3x-1 ------------- x²(x²+2)
What is A1 A2 B1x+C1 ---- + ---- + ---------- x x² x²+2
500
Use Gaussian elimination to solve the system of equations: x + z + w = 2 x + y + z = 3 3x+2y+3z+w = 8
What is (-z-w+2, w+1, z, w) ?