In Exercises 13 and 14 find a basis for the subspace spanned

In Exercises 13 and 14, find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace?

Solution

here we are given some vector

1st write these these vector as matrix having the vector as coloum and then solve it to get a piovot

means to find that how many of the vector are linearly independent.

here we will find 2 vector (1,-1,-2,5) and (2,-3,-1,6) are linearly independent.

so dimension of the subspace is 2.

and subspace spanned in R ,so the basis is (1,-1,-2,5) and (2,-3,-1,6)