Linear Algebra Quiz 1.4-1.7 Concept Check

If the equation Ax=b is inconistent, then b is not in the set spanned by the columns of A.

• True

• False

The homogeneous equation Ax=0 has the trivial solution if and only if the equation has at least one free vairable.

• True

• False

The equation Ax=b is consistent if the augmented matrix [ A b ] has a pivot position in every row.

• True

• False

A homogeneous equation is always consistent.

• True

• False

• True

• False

If x is a nontrivial solution of Ax=0, then every entry of x is nonzero.

• True

• False

If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S.

• True

• False

If x and y are linearly independent, and if { x, y, z } is linearly dependent, then z is in Span { x, y }.

• True

• False