Final answer:
To construct a 3x3 nonzero matrix A where the vector v = [6, 1, -1] is a solution to Ax=0, one can create a matrix with rows that are orthogonal to v. A possible matrix could be A = [[1, -6, 0], [0, 1, 1], [1, 0, -6]], as each row dotted with v equals zero.
Step-by-step explanation:
Assuming the vector is v = [6, 1, -1], we are looking for a matrix A that, when multiplied by v, gives the zero vector. This means that v should be in the null space of A. In order to create such a matrix, we need to ensure that each row of A, when dotted with the vector v, equals zero. Let's denote the rows of A as a1, a2, and a3. One possible way to construct this matrix is to choose rows that are orthogonal to the vector v. For simplicity, let's choose: a1 = [1, -6, 0] (Since 1*6 + (-6)*1 + 0*(-1) = 0), a2 = [0, 1, 1] (Since 0*6 + 1*1 + 1*(-1) = 0), a3 = [1, 0, -6] (Since 1*6 + 0*1 + (-6)*-1 = 0). Therefore, the matrix A can be: A = [[1, -6, 0], [0, 1, 1], [1, 0, -6]].