Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not need to do this in Sage and can type your answer directly onto your document. b. Find the maximum and minimum values of q(u) among all unit vectors u and describe the directions in which they occur. For part (b),

Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors ₁, ₂ in…

Q: (b) Write the following vectors as linear combinations of 21, 22, and 23.

Q: For the matrix H = Answer: 1 2 -1 2 0 51 13 find three different non-zero vectors that are in the…

Q: For each problem, give an example of a set of vectors in R4 that meet criteria and briefly justify…

Q: 2a 4 Span{-0} (a) Determine all real values a and b such that in R². (b) Determine the solution set,…

Q: Find a vector that is orthogonal to each of the three vectors below: 1 1 4 V1 = " V2 = 1 and V3 = 3…

Q: Let A = -1 -3 3 and b = b₁ 8} Show that the equation Ax=b does not have a solution for some choices…

Q: 4 A = 2 ( ) -3 Find a non-zero number 1 and a non-zero vector x so that Ax = 1x. Note: There are…

Q: 3. Find all real values of c such that the vectors and e+3 are linearly independent.

Q: X₁ Describe the solution set, x = x₂ X3 fill in the answer boxes within your choice. (Type an…

Q: Describe all solutions of Ax 0 in parametric vector form, where A is row equivalent to the given…

Q: 1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to…

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

Q: Find the matrix A of the quadratic form associated with the equation. 9x2 - 6xy +9y2 + 24z² - 29 = 0

Q: Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is…