Question

Let x,y,z be (non-zero) vectors and suppose ????=−2x−4y+3z. If z=x+2y, then ????= 1 x+ 2 y. Using the calculation above, mark the statements below that must be true.
A. Span(w, y) = Span(w, x, y)

B. Span(w, z) = Span(x, z)

C. Span(w, x) = Span(w, x, z)

D. Span(w, x) = Span(w, z)

E. Span(y, z) = Span(x, y, z)

Answer 1

Answer:

A. Span (w, y) = Span (w, x, y)

C. Span (w, x) = Span (w, x, z)

D. Span (w, x) = Span (w, z)

Step-by-step explanation:

The vectors x, y , z are non zero vectors. Vector has direction and magnitude both. For the given equation of -2x - 4y + 3z the span for w, y equals the span of w,x,y. The statements A, C and D are true and the other statements B and E are not correct. For the given equation the vector span y,z does not equals span of x,y,z.