FIRST EXAM-AInstructions:Begin each of the eight numbered problems on a new page in your answer book.Show your work, andmention theorems when appropriate.1.[15 Pts] Find the general solution of the following homogeneous system of equations. Express your answer using vectornotation. Use the method developed in class. What is an appropriate (mental) geometric picture for this solution set?±x1−3x2−9x3+5x4=0x2+2x3−x42. Determine which of the following sets of vectors are linearly independent. Give reasons for your answers.a.⎡⎣10−62⎤⎦,⎡⎣5−31⎤⎦b.⎡⎣1−2−1⎤⎦,⎡⎣000⎤⎦,⎡⎣3−5−4⎤⎦c.⎡⎢⎢⎣110−1⎤⎥⎥⎦,⎡⎢⎢⎣−21−35⎤⎥⎥⎦,⎡⎢⎢⎣1−12−3⎤⎥⎥⎦,⎡⎢⎢⎣09−44⎤⎥⎥⎦3. LetA=⎡⎣11−2−1−1−3⎤⎦,y=⎡⎣2−74⎤⎦, and de±neT:R2→R3byT(x)=Ax.
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