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Matrix Operations and Cramer's Rule: A Comprehensive Review

This review focuses on matrix operations, including addition, row operations, and determinant calculation. Students will also learn to solve systems of equations using Cramer’s Rule and Gaussian elimination. The test covers various matrix manipulations, such as performing row operations on matrices and converting sequences and series into summation notation. Additionally, students will find geometric series sums and the terms of given sequences. A thorough understanding of these concepts is essential for success in matrix algebra. Study hard and good luck!

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Matrix Operations and Cramer's Rule: A Comprehensive Review

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  1. MAC 1140 Unit 4 Test Review

  2. 1. Give the order of the following matrix: .

  3. Given the following matrices, perform the indicated operation if possible. If not possible, write NP in the answer blank. A = C = B = D = E = F = 2. A + B 3. BC 4. 3C + D 5. 6. BF 7. BE

  4. Perform the following row operations beginning with matrix B and using your answer to each matrix for the next. B = ___________________ 8. ___________________ 9. . __________________ 10. Write the remaining row operation it would take to get the 2 X 2 identity matrix

  5. 11. Given the following matrix , calculate the determinant.

  6. Solve for x using Cramer’s Rule. _______ 12. x – y = 1 ______ 13. 2x – 2y + 3z = 7 3x+y = 7 x + y – z = -2 3x + y – 2z = 5

  7. Solve the system of equations: Use any method. _________________ 14. x + y + z = 4 x + y – z = 6 x – y – z = 8 __________________ 15. x - 2y + z = -3 2x + 4y + 2z = 5

  8. ______________ 16. Solve using Gaussian elimination with your calculator: x – y + z = 5 x + y + 3z = 11 -x + 2y – z = -5

  9. 17-18. Given the geometric series: 2 + 6 + 18 + 54 + 162 • Write the geometric series in summation notation. • 18. Find the sum of the geometric series

  10. Given the following sequence: -5, -2, 1, 4, 7, …. . Find the • 41st term. • Determine the sum of the following sequence: • -6,-3,0,3,6,9,…,291 • 21. Find the sum of the geometric series: 1 + ½ + ¼ + …..

  11. STUDY HARD GOOD LUCK!!!!!!

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