Find the distance from y to the subspace W of set of real numbers R Superscript 4ℝ4 spanned by Bold v 1v1 and Bold v 2v2, given that the closest point to y in W is ModifyingAbove Bold y with caretyequals=[Start 4 By 1 Matrix 1st Row 1st Column 7 2nd Row 1st Column 5 3rd Row 1st Column negative 1 4st Row 1st Column 4 EndMatrix ]7 5 −1 4 .

Step-by-step explanation:

And according to the information given the closest point to in W is

This is a problem when they give you more information than you actually need, by definition the distance from a vector to a subspace is given as the distance to the closest vector of the subspace, usually you have to find the vector using the Gram-Schmidt process and the orthogonal projection of the vector to the subspace, for this case you do not need any of that because the vector is given so all you find is the distance between which is

nope

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.