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Algebra 3 Chapter 4 Practice Test Name ______________________________ Per. __ Date ___ _ Matching: Find the word or phrase in the word bank that best completes the statements for problems (1 – 5). WORD BANK: A) Identity Matrix B) Element C) Scalar D) Rows E) Inverses Problem F) G) H) I) Columns Determinant Matrix Dimensions 1. Statement [−2 6 0] 3, Given the matrix the 3 on the outside of the matrix is called a ____________ 2. Given the matrix [ 3. The matrix [ 4. To prove if the inverse of a matrix exist, you can use the _____________________. 5. In a matrix, the numbers arranged vertically are called the ___________________. 6. A(n) _____________ is a rectangular array of constants or variables. 7. The __________________of a matrix with 4 rows and 3 columns are 4X3 8. If the product of two matrices is the identity matrix, they are _________________. 3 −4 ], -4 is called a(n)_____________________of the matrix. 0 5 1 0 ] is an example of a(n)__________________ 0 1 Multiple Choice: Bubble in your final answer on the answer document. 9. How many element s are in a 3𝑋3 matrix? 10. 1 Find the value of element 𝑀13 , 𝑀11 , 𝑎𝑛𝑑 𝑀22 if 𝑀 = [ 4 11. 4 If P = [ 2 1 1 ] and Q = [ 0 0 6 ], what is 𝑄 − 𝑃? 2 2 3 ] 5 6 Algebra 3 Chapter 4 Practice Test 12. 13. 6 If S = [ 3 If P = [ Name ______________________________ Per. __ Date ___ _ −4 9 ], what is 3𝑆 ? −1 −5 4 1 0 ] and R = [ 2 0 1 1 2 −2 ], what is 2𝑃 + 4𝑅 ? 14. 2 If M = [ 2 2 6 1 ] and N = [ ], what is 𝑀 − 𝑁? 2 2 0 15. 3 What are the dimensions of the product of X and Y where X= [[3 4]] and Y = [ ]? 2 16. Given P = [ 17. −2 3 1 2 Find the product if possible. [ 4 ]. 0 ]∙ [ 2 1 1 −5 18. Find the determinant for [ 19. Find the determinant for [ 20. 2 1 6 Find the determinant for [−2 4 3 ]. −1 5 −3 3 0 −2 1 ] and R = [ ], find PR. −1 −3 1 0 3 −2 ]. −5 6 −9 7 ]. 6 −4 Algebra 3 Chapter 4 Practice Test 21. 22. 23. Name ______________________________ Per. __ Date ___ _ Find the area of a triangle with vertices (2,4) , (−3, −2) , 𝑎𝑛𝑑 (3,0) using the determinant. 1 If C = [ 5 0 ] 𝑎𝑛𝑑 D = [ 5 0 1 0 3 Find the inverse of [ 5 0 1 ], determine if matrices C and D are inverses of each other. 0 ]. 1 Inverse Formula: 𝐴=[ 𝐴−1 = 24. 3 5 Does the inverse exist for the matrix [ ]? 6 3 25. Solve for 𝑥 and 𝑦 using the inverse matrices. See inverse formula on #20 2 −1 𝑥 −9 [ ] ∙ [𝑦] = [ ] 1 2 8 26. What is the value of 𝑚 ? −2 3 8 0 5𝑚 −3 [ ]+[ ]=[ ] 4 6 4 12 0 6 27. What is the value of 𝑛 ? 3 22 9 −3 −6 25 [ ]−[ ]=[ ] 2𝑛 10 7 6 13 4 28. What is the x-coordinate of the solution to the system of equations: 2𝑥 − 5𝑦 = 15 { 3𝑥 − 6𝑦 = 36 𝑎 𝑐 𝑏 ] 𝑑 1 𝑑 [ −𝑐 𝑎𝑑 − 𝑏𝑐 −𝑏 ] 𝑎 Algebra 3 Chapter 4 Practice Test Name ______________________________ Per. __ Date ___ _ 29. What are the solution(s) for 𝑧 ? |5𝑧 − 6| = 14 30. Solve the absolute value inequality |3𝑤 − 5| ≤ 4 31. Write the equation of the line in slope-intercept form that passes through the points(2, 6) 𝑎𝑛𝑑 (1, 1). 32. Graph the linear inequality 2𝑥 + 3𝑦 > 6 ? 33. Solve for 𝑥 2(5 − 𝑥) = 4𝑦 Scan here for extra help!