Consider the matrix A 2 (i) Find the characteristic equation of A. (ii) Diagonalise A by computing D, V and V-1 such that A = VDV-¹, where D is a diagonal matrix. (iii) Find A" for all positive integers n.

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

A:

Q: A tank that can hold 500 gal. originally contains 200 gal. of water with 100 Ibs. of salt in…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Solve the matrix equation AX + C = AXB there 1 2 a) A = (-1 ½) · B - (-6 3 ) a = and C = 27 5-1 -22…

A:

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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: Each of the following statements is either true or false. Determine for each one whether it is true…

A: e. True: Let's consider the rational number a=0 and the irrational number b=2. The product ab=0×2=0…

Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

A:

Q: Find the matrix for T(w) = proj, where = [4 8 -2].

A:

Q: Let A, B be two matrices with linearly independent columns. If Col(A) = Col(B) then A(AT A)-1 AT =…

A:

Q: 3. Find m and n so that the matrix below is symmetric:

A:

Q: Find the characteristic equation of the given matrix: 8. -D1 2 0. A = 8 -D1 6 -6 1 6 5 Select one: O…

A:

Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: 3.) Find the inverse matrix? 2 Use the adjugate of A = 0 -2 1 to find A-1 | 1 0 0 - 2 3.

A:

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find a P'LU factorization of the given matrix A. (Enter each matrix in the form [[row 1], [row…

A:

Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

A: 5000050000-30000-3

Q: Diagonalize the quadratic form by finding an orthogonal matrix Q such that the change of variable…

A: Given Quadratic form is  Q=6x12 +9x22 -4x1x2                            ⇒…

Q: Express the quadratic equation in the matrix form x Ax + Kx + f = 0, where a Ax is the associated…

A: The given quadratic expression is .We need to convert this quadratic in the form .

Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

A:

Q: Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5   3]       B=[3   −6] [4.25…

A: