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4 Feb 2018

3. 181 Compute the determinant of the following matrix. You may use any available technique and you may use the properties of determinants to simplify the matrix 4 -13 11 2 2 6 01 A= -10-31 | 4 1 120

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Keith Leannon
Keith LeannonLv2
5 Feb 2018
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2. Las=[{ 1 }].5-() 6 - (3) . -- (1) to make 2. Let A = [ 2 3 -11 1 1 1 .6 (01 2] -1 = 0 , and = | y 8 marks). (a) Write out the augmented matrix which represents the system of linear equations: (A - XI) = 5 (b) Rewrite the augmented matrix derived in (2a) with: i. 5= 0, 1 = 1. ii. 5= 0, 1 = 2.

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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