QUIZ 1 ANSWERS1.10412-1x1x2=b1b2b3.a).(12 points) We reduce:10b141b22-1b3→10b101b2-4b10-1b3-2b1→10b101b2-4b100b3+b2-6b1.So the equation becomes:100100x1x2=b1b2-4b1b3+b2-6b1.b)(6 points) Only whenb3+b2-6b1=0.2. a)(8 points) Solutions toAare length 3 column vectors, soAhas three columns.b)(8 points) Any number. In fact consider(1-c-d). This kills both of the givenvectors. Then, feel free to add any number of rows of zero’s below it.c)(8 points) We assume that the matrix is not zero as we are given that these are theonly special solutions. To find the rank, we note that each row ofAmust be in the subspaceofR3which is orthogonal to(c10)and(d01), but since these guys span a plane,this subspace is a line. Thus the rows are all linearly dependant, and so the rank is one.3. a)
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