Question

A system of linear equations Ax=b is consistent if b is in a) the null space of A b) the row space of A c) the column space of A d) the range of A.​

Answer 1

Given:

A linear equation Ax = b

To find:

Condition for its consistency

Proof:

• The given equation Ax = b is consistent if and only if b is in the column space of A.

• We can infer from the consistent equation Ax=b that x₁, x₂, . . . ,xₙ are satisfying the equation.

• This implies that b is in the column space of A.

Answer 2

Answer:Given:

A linear equation Ax = b

To find:

Condition for its consistency

Proof:

The given equation Ax = b is consistent if and only if b is in the column space of A.

We can infer from the consistent equation Ax=b that x₁, x₂, . . . ,xₙ are satisfying the equation.

This implies that b is in the column space of A.

Step-by-step explanation: