2 38. Use Gauss-Jordan Elimination to solve the system of linear equations marks + y + 2x = 1 2.0 + 2y + 4z = 2 - - y - 22 = -1 Express your answer in vector form. Show your work.

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A 40. Use Cramer's rule to find the value of 2 in the solution to the system of linear equations marks shown below. Show your work. I 2.0 -2 + 2y + + 5y + + y + 2 z 2x = = = 3 1 6

1. Put the following system of equations into an augmented matrix and perform row opera- tions to get the matrix into Row Reduced Echelon Form. Give your answer as r = ..., y = ...,2= .... Marks will be deducted if you leave your solution in matrix form! IF the system is inconsistent, it is sufficient to only Row Reduce, and then clearly state your findings [22 marks]. (a) 2.r + 3y - 2 1 + y +2 y - 22 = = = 4 3 -1 11 +262 +23 – 3.04 = 2.0 +6.02 + 3.03 - 24 = -X1 + 12 + 2.24 = ri +12 +13 + 3.04 = 1 Ti + 2x2 - 3.13 +224 = -3.01 - 672 +2.13 - 14 = 12 + 2.13 +2 = -Ii - 22 - 2.13 + 4.14 ܝܙ ܨܝܝ

3. Consider the system of equations represented as the matrix equation, AT = b[12 marks]. (a) Use the method of inverses to solve the system of equations, and clearly show your answer: 5.0 – 2y = 1 -4.x + 2y = 2 (b) If A-1 = [14-11 11 2 O 3 , and 5 = | 2 ), then evaluate . Clearly show your answer. [ 7 2 1] (c) If 4-1 - 2 31 1 2 , and b then what is the ORIGINAL system of equa- tions?

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2 38. Use Gauss-Jordan Elimination to solve the system of linear equations marks + y + 2x = 1 2.0 + 2y + 4z = 2 - - y - 22 = -1 Express your answer in vector form. Show your work.

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