Please explain and solve number 5 Determine whether the set

Please explain and solve number 5

Determine whether the set S is linear independent or dependent. a.S = {(l, -4,1), (6, 3, 2)} b. S = {x^2 -1, 2x + 5} d. Let u, v, and w be linearly independent vectors. Determine whether the set of vectors { v - u, w - v, u -w} is linearly independent or linearly dependent. 5. Determine the set S is a basis for V. 6. Find a basis for the subspace of R\" spanned by S = {(6, -3, 6,34), (3, -2, 3, 19), (8, 3, -9, 6}} 7.a Find the coordinate matrix of x = (5,28,13) in R^3 relative to the basis B = {(5,11,0), (8,0,8), (1, 2,7)}, b.Find the coordinate matrix of p = x^2-15x + 2 relative to the standard basis in P_2. 8. Given bases B = {(1, 0, 0), (0,1,0), (0,0,1)} and B\' = {(1, 0,1), (0, -1, 2), {2, 3, -5)}, Find

Solution

5).

take the first matrix and then

a *1st colum values + b *2nd column value =0 (for in V=M22) (here a,b any constants)

a [1,0] +b[1,0] =0

a=0 , b= any value

here we can\'t decide wether this vector are in basiss of M22

so go for 3 matrix values

a[1,0]+b[0,1]=0

a=0 ,b=0

this is in M22 (since a,b=0)

b).

similer to the above one

a (3,6,4) +b(0,3,5)+c(0,0,7) =0

so 3a+0b+0c=0

3a=0 ,so a=0

second equation 6a+3b+0c=0

6(0)+3b=0

so b=0

third equation 4a +5b+7c=0

s0 4(0)+5(0)+7c=0

c=0

so a,b,c are zero so the vectors are in R^3