Find the coordinate vector of x relative to the basis B and

Find the coordinate vector of x relative to the basis B and C.

Find the coordinate vector of x relative to the basis B and C.

Solution

Let the elements of B be B1, B2 and B3 and that of

C be C1, C2 and C3.

Then x = aB1+bB2+cB3

Equate the corresponding elements to get

1 = a

0 = b

-1 =c

Hence coordinates of x wrt B are (1, 0, -1)

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x = pC1+qC2+rC3

Equate corresponding elements to get

1 = p

0 = p+q or q =-1

-1 = p+q+r

r =-1

Hence coordinates of x are (1,-1,-1)