Question

Find a basis for and the dimension of the subspace w of R4. w = (4s - t, s, 2t, s): s and t are real numbers. What is a basis for the subspace w of R4?

Answer 1

To find a basis for the subspace w of R4 and its dimension, set each component of w equal to zero. The basis for w is {(0, 0, 0, 0)} and the dimension of w is 0.

Step-by-step explanation:

To find a basis for the subspace w of R4 and its dimension, we need to solve for the values of s and t that make the equation of w equal to zero.

The equation for w is (4s - t, s, 2t, s). Setting each component of w equal to zero, we get 4s - t = 0, s = 0, 2t = 0, and s = 0. From these equations, we can see that s = 0 and t can be any real number. Therefore, a basis for w is {(0, 0, 0, 0)} and the dimension of w is 0.