Ch. 5 - Systems and Matrices
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- Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 2x + 6y = 6 5x + 9y = 9
Problem 1
- What is the value of ?
Problem 1
- How many rows and how many columns does this matrix have? What is its dimension? <4x2 Matrix>
Problem 1
- What expression in x represents ?
Problem 3
- What is the augmented matrix of the following system? -3x + 5y = 2 6x + 2y = 7
Problem 3
- Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 1/6x + 1/3y = 8 1/4x + 1/2y = 12
Problem 4
- What is the value of x if = 9?
Problem 5
- Solve each system by substitution. See Example 1. 4x + 3y = -13 -x + y = 5
Problem 7
- Evaluate each determinant. See Example 1.
Problem 7
- Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -4 times row 1 added to row 2
Problem 7
- Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -7 times row 1 added to row 2
Problem 8
- Solve each system by substitution. See Example 1. x - 5y = 8 x = 6y
Problem 9
- Evaluate each determinant. See Example 1.
Problem 9
- Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.
Problem 9
- Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 2 times row 1 added to row 2
Problem 9
- Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 4 times row 1 added to row 2
Problem 10
- Evaluate each determinant. See Example 1.
Problem 11
- Solve each problem. Alcohol MixtureBarak wishes to strengthen a mixture that is 10% alcohol to onethat is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?
Problem 11
- Solve each system by substitution. See Example 1. 7x - y = -10 3y - x = 10
Problem 13
- Evaluate each determinant. See Example 1.
Problem 13
- Write the augmented matrix for each system and give its dimension. Do not solve. 2x + y + z - 3 = 0 3x - 4y + 2z + 7 = 0 x + y + z - 2 = 0
Problem 13
- Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0
Problem 14
- Solve each system by substitution. See Example 1. -2x = 6y + 18 -29 = 5y - 3x
Problem 15
- Evaluate each determinant. See Example 1.
Problem 15
- Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>
Problem 15
- Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.
Problem 16
- Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2
Problem 17
- Find the cofactor of each element in the second row of each matrix. See Example 2.
Problem 17
- Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>
Problem 17
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 4x + y = -23 x - 2y = -17
Problem 19
