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1. Consider a linear system of equations whose augmented matrix is 1 1 3 2 1 1 2 43 11 3 alb (a) Reduce the augmented matrix to echelon form. [4 marks) (b) For what values of a and b will the system have infinitely many solutions? [2 marks] (c) For what values of a and b will the system have a unique solution? (2 marks] (c) For what values of a and b will the system have no solution? [2 marks]

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Lelia Lubowitz
Lelia LubowitzLv2
31 Dec 2017
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Related questions

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

4. A linear system is represented by the following augmented coefficient matrix 1-1 -32 0 2 21-11 0 1 11-1 How many solutions will this linear system have? A) no solutions B)exactly one solution C)exactly two solutions D)infinitely many E) none of these

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.

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