linear combination urgent help

Let *A*= . -1 1 -1 3

3 1 -1 -1

2 -1 -2 1

**a) **Find a matrix *B* that is row equivalent to *A*.

**b) **Determine whether the fourth column vector forms a linear combination with the first three column vectors.

**c) **Show that the first three column vectors are linearly independent. Explain.

i need help to practice this i have test day after tommorow..i need hard pracrice///(Nerd)(Nerd)(Nerd)(Nerd)(Nerd)(Nerd)(Nerd)(Nerd)

Re: linear combination urgent help

For a), just do any of the row operations and that matrix will be row equivalent to A.

For b), Just set the equation up, $\displaystyle a[-1 \ 3 \ 2]^T + b[1 \ 1 \ -1]^T + c[-1 \ -1 \ -2]^T = [3 \ -1 \ 1]^T$

Where T refers to the transpose. solve for a, b, and c. You could even use a few guesses to see what you get, if you wanted.

For c), You need to show that the first three column vectors satisfy this property:

A set of vectors, $\displaystyle v_1,v_2,v_3,\cdots,v_n$ are linearly independent if and only if $\displaystyle a_1v_1 + a_2v_2 + a_3v_3 + \cdots + a_nv_n = 0$ implies that $\displaystyle a_1 = a_2 = a_3 = \cdots = a_n = 0$.

Re: linear combination urgent help

i was having much problem in b now i just finished doing this.thankyou so much.may god bless u.