Exam 8: Systems of Linear Equations and Inequalities

Write the matrix in row echelon form.

Apply the matrix algebra to solve the system of linear equations. 5r - 2s + 2t = -11 -2r + 3s + 6t = -2 5r - 2s + 2t = -5

Apply the matrix algebra to solve the system of linear equations. 8r - 7s - 2t = 34 -4r + 7s + 5t = -5 -6r - 7s - 7t = -51

Solve the system of linear equations by graphing the following equations. 7x + 6y = 63 8x + 5y = 59

Find the partial-fraction decomposition for the rational function.

Write the system of linear equations as an augmented matrix. 2x - 23y + 15z = -20 -13x + 26y + 29z = -11 8x - 6y - 25z = -17

If three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) are collinear (line on the same line), then the following must be satisfied. Determine whether (6, -10), (16, -1), and (-4, -19) are collinear.

Write the system of linear equations as represented by the augmented matrix. Utilize the variables x, y, and z.

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Solve the system of linear equations by elimination.

Determine if B is the multiplicative inverse of A using and

Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solution), or dependent (infinitely many solutions). 7x - 10y + 5z = -50 -7x + 10y - 5z = -1 8x + 8y - 10z = -46

Solve the system of linear equations by elimination. 2d + 6f = 4 -2d - 5f = -5

Calculate D(A + B) if , , and

Write the system of equations as represented by the augmented matrix. Utilize the variables x and y.

Write the partial fraction decomposition for the given rational expression.

Solve the system of linear equations for x, y, and z.

Solve the system of linear equations by substitution. -8p - 3q = -48 -16p - 6q = -96

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Solve the system of equations.