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Midtest

# Midtestmas3105 page 3 of 5 3 18 pts a write the

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MidTest/MAS3105 Page 3 of 5 3. (18 pts.) (a) Write the general solution of the system of equations x 1 -6 x 2 +8 x 3 =5 x 1 x 2 -8 x 3 =- 5 in parametric form. (b) If A = 1- 6 8 6- 8 , Nul(A) is a subspace of k for which k ? k= (c) Using your results from part (a), give an explicit description of Nul(A). (d) Is the linear transformation T: 3 2 defined by T( x )=A x , where A is as in part (b), onto? Explain. (e) When T is the linear transformation of part (d), what is the kernel, ker(T), of T ? Use all the information you have at hand. ker(T) = (f) What can you say about the column space of the matrix A of part (b)? Why? Explain as completely as possible. Col(A) =

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MidTest/MAS3105 Page 4 of 5 4. (10 pts.) (a) For which value(s) of s does the following equation, have a unique solution ? s1 - 2  x 1 1 0 s-2 1  x 2 = -2 00 3 s  x 3 3 (b) When the equation in (a) has a unique solution, obtain x 2 in terms of s when x is that unique solution. (Hint: Cramer’s rule might be simple enough here.) 5. (10 pts.) Suppose that A isa6x6 matrix with det(A) = -10. (a) When B is obtained from A by replacing row five with negative twenty-nine times row three plus row five, then det(B) = .
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MidTestMAS3105 Page 3 of 5 3 18 pts a Write the general...

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