1. (10 points) Find the general solution of the following linear system 2.11 +02 - 13 - 14 = 3.01 +12 +13 - 2.04 = -01-12 +2.13 + 14 = - 2xı -12 + 2x4 = -1 -2 2

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adieLv10

17 Apr 2022

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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. [10 marks) Let T:R' RP be the linear transformation defined by I = 2:01 - 403 22-23 + 3.74 Il +.12 - 3.13 +2.04 ) (a) Find the image of the vector, ID=|| i by applying the given transform, T. (b) Find the standard matrix of T. (c) Find the image of rd (above) by matrix multiplication of the standard matrix of T and rp. Compare your answer to (a). (d) Find the vector from the domain, cd, which gives the image cr=| 1 in the range of T.

3. (10 points) Use Cramer's rule to find the value of 13 from the solution to the following linear system: I1 - 202 – 2.63 = 7 22+273 = 4 +I3 = 0. No other method will be accepted.

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1. (10 points) Find the general solution of the following linear system 2.11 +02 - 13 - 14 = 3.01 +12 +13 - 2.04 = -01-12 +2.13 + 14 = - 2xı -12 + 2x4 = -1 -2 2

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