# linear combination urgent help

• Dec 7th 2013, 05:05 AM
rabia123
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)
• Dec 7th 2013, 08:28 AM
Aryth
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\$.
• Dec 7th 2013, 10:41 AM
rabia123
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.