2. H -1. Use the matrix formed by {₁, 2, V3} to 5 determine whether the {₁, 2, 3} spans R3. Explain how to use Theorem 4 to justify your answer. Let ₁ ---- = -3 and 3 = = x

Q: B=" Let A = [_12] and B-[ 2 4 -2 35 determinants Compute @ without using Bb Solve Ax=b where b = [i]

A:

Q: 9. 4 -6 -21 7 3. 8 -3 4 -7 8 8 0 13 17 31 7 9 4 23 4. -6 11 0 3 6 0

A:

Q: Give example 2. Determinant of a 5 × 5 matrix using properties of determinants

A: The solution of the problem is given in the next steps.

Q: Example: f=(f¹, f²): R³ → R² (-6) T1I2X3 that is, f¹(x) = x₁²² and ƒ²(x) = 1₁T2Tz. Then the Jacobi…

A:

Q: Q2. For the matrix, A = (a) Find 2 Tr (2 A). (b) If A = 21 8 7 4 6 7 5 4 find (A)-².

A:

Q: 3. Let B = {[4] [7]} and c={[7][7]} 4 9 C a. Find the change of coordinate matrix from C to B.

A:

Q: 12.) Find the determinant of A= -2 3 1 57 -1 2 0 4 1 0 TN -2 1 3 -3 4 Show your work.

A:

Q: 2. Let B = {v₁ =, √₂ =, V3 =, V4 =}. Use determinant to determine whether B is linearly independent…

A:

Q: 2. Find the determinant for (1 3 b) B =-5 2 1 -8 - 2 0 3 4) a) A = -1 -3 1 (-5 2 1 4.

A:

Q: 4. Express the following statements in one of the forms P V Q, P ^ Q, or ~ P. Be sure to clearly…

A: (a) Let P be the statement  P: The matrix A has zero determinant  Therefore , the given statement :…

Q: 6) Find the determinant: -2 3 4 3 4-2 5 6-3

A:

Q: Compute the quadratic form x¹Ax for the given matrix A and vector x. [59 0] A = 91 4, X = X2 04-2 x3…

A:

Q: Use the determinant to decide whether the matrix B given below is singular or nonsingular. B-/14 14…

A:

Q: B= 4 7 8. A= 2. Find 1-Matrix C. 3B 2- Matrix D - AB inNN

A: Given A=352252 and B=204768C=3B=3*204768               C=[6012211824]

Q: 4. Determine if the following sets are linearly independent or linearly dependent. Justify your…

A:

Q: 24. The inverse of a 3×3matrix may be found by -3 4 25. Determine the matrix AxI, A= and transposing…

A: Transpose is an operation in matrix algebra. When we interchange the rows and columns of a matrix,…

Q: For each of the following, factor the matrix A into a product QDQ' where Q is orthogonal and D is…

A: A is symmetric matrix ,then A is orthogonally diagonalizable, and Q is the orthogonal matrix, the…

Q: Find the matrix representations for R² and R-1.

A: First we define relation matrix for R:

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

A:

Q: X₁ Describe the solution set, x= x₂ of x₁ + 6x₂ - 2x3 = -7 in parametric vector form. Select the…

A: A set x=x1x2x3 of x1+6x2-2x3=-7. To Find: Describe the solution set x in parametric vector form.

Q: 3. Let vi = [1, -2,3], v2 = [-1,–4,5], and v3 = [5,-1,3] be vectors in R³. a) Use determinant to…

A:

Q: 0 -2 2 -1 B = 1 4 -1 3 4

A: We have to solve given problems: