Linear Algebra Answers

"\\begin{Bmatrix}\n a \\\\\n b\n\\end{Bmatrix} = 1\/314*\\begin{bmatrix}\n 198 & -26 \\\\\n -26 & 5\n\\end{bmatrix}\\begin{Bmatrix}\n 1230 \\\\\n 6950\n\\end{Bmatrix}"

find the values for x, y, and z such the matrix below is skew symmetric.

0 x 3

2 y -1

z 1 0

Consider the real space R³

 The following vectors form a basis S of R^3:

u1 = (1, −1, 0), u2 = (1, 1, 0), u3 = (0, 1, 1)

Find the coordinate vector [v] of v = (5, 3, 4) relative to the basis S .

Determine whether the polynomial x²+2y²+4xy+2yz+6xz is a quadratic form and if so write it in the form X^T AX, where A is a symmetric matrix.

By examining the determinant of the coefficient matrix, show that the following system has a nontrivial solution if and only if α = β

x + y + αz = 0

x + y + βz = 0

αx + βy + z = 0

If the characteristic polynomial of a matrix A is p(λ) = λ²+ 1, then A is invertible

An n x n matrix with fewer than n distinct eigen values is not diagonalizable

inverse of 1 2 3

4 5 3

7 8 9

Let 𝑆 be any non-empty set and let 𝑉 (𝑆) be the set of all real valued functions on ℝ. Define addition on 𝑉 (𝑠) by (𝑓 + 𝑔)(𝑥) = 𝑓 (𝑥) + 𝑔(𝑥) and scalar multiplication by (𝛼 ⋅ 𝑓 )(𝑥) = 𝛼𝑓 (𝑥). Check that (𝑉 (𝑆), +, ⋅) is a vector space.

Show that if W consist of these vectors (a, b, c)€R³ for which a=2b then W is subspace of R³