Question

Construct a 3x3 nonzero matrix A such that the Vector [-1 -1 -1] is a solution of Ax=0

Answer 1

To construct a 3x3 nonzero matrix A such that the vector [-1 -1 -1] is a solution of Ax=0, one possible matrix A is [-1 -1 -1].

Step-by-step explanation:

To construct a 3x3 nonzero matrix A such that the vector [-1 -1 -1] is a solution of Ax=0, we need to find a matrix A such that when multiplied by the vector [-1 -1 -1], the result is the zero vector [0 0 0].

We can represent matrix A as:

A = [a b c]

Different values of a, b, and c will result in different matrices A, but in order to satisfy the equation Ax=0, we need to have:

• a(-1) + b(-1) + c(-1) = 0

Simplifying the equation, we get:

• -a - b - c = 0

One possible solution is to assign values to a, b, and c such that the equation is satisfied, for example:

• a = -1, b = -1, c = -1

Therefore, one possible matrix A that satisfies the given condition is:

A = [-1 -1 -1]