Let the vector system U = {(1,2, 9); (0,-1,-8);(2,3,10);(1,0,-7)} a. Find the number of dimensions and a basis W of the subspace generated by the vector system U .
b. Find the parameter x so that u=(2,3,+1) is a linear combination of W , and derive [U]w.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

eight hundred an fifty one point four hundred and fifteen

800+50+1+.4+.01+.005