Question

Construct a 33 nonzero matrix a such that the vector is a solution of ax0.

Answer 1

To construct a 3x3 nonzero matrix A such that the vector x = (0,0,1) is a solution of Ax=0, one possible matrix is A = [[1, 0, 0], [0, 1, 0], [0, 0, 0]]. When this matrix is multiplied by the vector x, the resulting product is the zero vector [0, 0, 0].

Step-by-step explanation:

To construct a 3x3 nonzero matrix A such that the vector x = (0,0,1) is a solution of Ax=0, we need to find a matrix A such that when multiplied by the vector x, the resulting product is the zero vector (0,0,0).

One example of such a matrix is:

A = [[1, 0, 0], [0, 1, 0], [0, 0, 0]]

When we multiply this matrix A by the vector x = (0,0,1), the product is:

Ax = [[1, 0, 0], [0, 1, 0], [0, 0, 0]] * [0, 0, 1] = [0, 0, 0]