Linear Algebra Answers

Let U, V be subspaces of R^n. Prove that U + V = {u + v : u ∈ U and v ∈ V} is also a subspace of R^n.

Determine which vectors in R^4 belong to both span{(1, −2, −2, 3), (−1, 3, 1, −2)} and span{(0, 1, 0, −1), (1, −3, 0, 0)}.

[img]https://upload.cc/i1/2020/03/11/FeuSgt.jpg[/img]




the digit number R is 4

Find a non-zero unit vector u with terminal point Q(-7,4,4) such that u has the opposite direction as v=(3,2,1)

Graph this equation by plotting three points: y = 3x - 2.




What are your points?


Where does your line cross the x-axis(write as an ordered pair, or if it is not a "nice" point, provide the two numbers it lies between)?


Where does your line cross the y-axis(write as an ordered pair)?


Is the origin on the right or left side of the line?

Find the orthogonal canonical reduction of the quadratic form -x²+y²+z²+xy+xz− 6

Find the orthogonal canonical reduction of the quadratic form

-x²+y²+z²+xy+xz-6yz

. Also, find its principal axes.

The Gaussian elimination method can only be applied for solving a system of 4

linear equations if the number of variables is 4. Is it true or false ? give reasons.

For the vector space P2,find the dual basis of {1+x,1+2x,1+x+x2}?

Let A = (a ij) n x n, where n >= 3, such that a ij = i - j for each 1 <= i <= n and 1 <= j <= n. Prove that det(A) = 0