Math121 Discussion - 4th week (revised)

# Math121 Discussion - 4th week (revised) - A-1 or C-1(d Show...

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MATH 121 DISCUSSION WEEK 4 WORKSHEET 1) Show that the system of equations below has no solutions. 2 x + 5 y - 2 z = 5 - x - 2 y + 4 z = - 4 - y - 6 z = 5 2) Consider the system of equations below. x + 3 y + 5 z = 2 x + 4 y + 7 z = 6 - 2 x - 4 y - 6 z = 4 (a) Rewrite the system as a matrix equation of the form AX = B. (b) Show that the system above has an inﬁnite number of solutions. (c) Write a general solution for the system in terms of z . 3) Consider the below matrices. A = ± 7 - 4 3 5 0 1 ² ,B = 4 6 - 2 ,C = 6 - 8 - 10 1 3 4 ,D = ± 8 5 2 1 - 1 6 ² E = ± 1 2 - 7 4 - 2 7 ² (a) Solve (4 A - 3 D ) B . (b) Solve A ( CD ) + 5 A . (c) Explain why we cannot ﬁnd
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Unformatted text preview: A-1 or C-1 . (d) Show that E-1 does not exist. (e) Suppose we are given the matrix equation, EX = (AB) where X = ± x y ² . First, write out the complete expression for EX = (AB). Then rewrite this as a system of linear equations. 4) Using matrix equations, solve the following systems of equations. (a) Find the solution for this system. 4 x-y = 3 2 x + 5 y =-9 (b) Find the solution for this system.-9 x + 4 y =-13-6 x + 3 y = 1 1...
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