Algebra II B Give the dimensions of the matrix. 1. [ 1 2 0 1 Name______________________ Chapter 11.1-11.3 Practice Quiz −5 ] 3 1 0 2. [0 1 0 0 8 0 5 −1] 0 0 3. [5 6 1] _______________ _________________ ______________ Use the following matrices to perform the indicated operation, or explain why it cannot be done. (No Calculator!) 𝐴 = [2 1 0 −1] 𝐵 = [ −2 2 1 4 ] 0 0 𝐶=[ 2 −2 4. D+C 𝐴 = [2 3 −1] 1 1 𝐷 = [0 2 4 −1] 0 𝐸=[ 2 −5 −1 ] 6 5. 2E 1 0 −1] 𝐵 = [ −2 2 1 4 ] 0 0 𝐶=[ 2 −2 3 −1] 1 4 𝐹 = [−1 7 0 1 5 2 0] 0 𝐺=[ 4 2 −3 ] 0 2 0] 0 𝐺=[ 4 2 −3 ] 0 6. C - 4D 1 𝐷 = [0 2 7. 5E – 2B 8. AB 10. BC 11. EF 4 −1] 0 𝐸=[ 2 −5 −1 ] 6 4 𝐹 = [−1 7 0 1 5 9. EG 12. AC 𝟏 Find the inverse, if it exists. Use the formula 𝑨−𝟏 = 𝒂𝒅−𝒃𝒄 [ 13. 𝐸 = [ 2 −5 −1 ] 6 𝒅 −𝒃 ] −𝒄 𝒂 2 14. 𝐸 = [ −3 −4 ] 6 Use the rule 𝑿 = 𝑨−𝟏 ∙ 𝑩, (where A is the coefficient matrix, X is the variable matrix and B is the known matrix), to solve the following systems of equations. 15.  4 x  8 y  24  x  3 y  9 16. You attend a movie with a group of people. Each adult ticket cost $15, and each childs ticket costs $10. There are 15 people in your group, and the price of the tickets is $175. How many adults and children are in your group? Set up a system of equations and use matrices to solve. 17. If the dimensions of 𝑴𝒂𝒕𝒓𝒊𝒙 𝑨 𝒊𝒔 𝟒𝒙𝟑 and the dimensions of 𝑴𝒂𝒕𝒓𝒊𝒙 𝑩 𝒊𝒔 𝟑𝒙𝟕, then the dimensions of 𝐀 ∙ 𝐁 is: A. 3x3 B. 4x3 C. 4x7 D. impossible

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