8 -2 -2 A -3 3 -6 3 15 Find a matrix S and a diagonal matrix D, such that S-1 AS = D. Hint: det(A – AI) = (9 – A)2(8 – X).

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: If A is 4x4 matrix with det(A)=10, find det (24-¹A), det (A²).

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Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: 1 3 -1 For the given matrix A=-2 1 2. Find the inverse matrix ? 053

A: From the given problem:   AT=13-1-212053 So,   A=1-20315-123

Q: D = 3 1 5 0 -4 5 -2 -4 3

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Q: Q1: Given that A = [3 -3 -5] and B = 5,what is the matrix A- BT?

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Q: Consider the following matrices: -7 M = -1 (4-2) and (NM) - (34) 2 7 T = 1 a) Find matrix N. b)…

A: Step 1: Step 2: Step 3: Step 4:

Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: Solve A x A T matrix: A = -2  1  -1 3   -3   2

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Q: Q8: Given that -2 X = 1 8 -8 -9 -9,Z -7 7 -2. -8 5 what is the matrix 3X + Y – 3Z?

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Q: Q4: If the matrix A = (; :),s Show that A2- 2A – 21 = 0.

A: We observe that characteristics eqn of A will be x^2-2x-2=0. By Caley hamilton tum put x=A we get,…

Q: Find a 2 × 2 matrix that maps e₁ to -3e2 and e2 to 2e1–e2.

A: The 2x2 matrix that maps e1 to -3e2 and e2 to 2e1 - e2 is [02​−3−1​]Explanation:

Q: Ak = PDP-1 (a) Show by mathematical induction that for a n x n diagonal matrix D with diagonal…

A: Let us prove the given result by induction or by taking induction on order of diagonal matrices.

Q: Given 2. A and B = ( 4 Find the matrix represented by: (iii) 3(A – 4B) (iv) B+ 3AT

A: The given matrices are A=254-2  and B=-1724. (iii) Evaluate 3(A-4B) as follows.…

Q: Find matrix A, given that: :) 8. -2 2A-1 10 9.

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 2 take inverse on…

Q: Determine the rank of matrix A, where: A = 1 0 -1 39 0 0

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Q: The first derivative of f(x) = 10x³ - 3 (5x4 - 6x)³ C. (3-10x³)√(5x4 - 6x)³ A. Select one: OA OB ос…

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Q: Q2: Find the inverse of the matrix M =

A: The given matrix is: M=-312-1 Formula: The inverse of the matrix A=abcd is: A-1=1ad-bcd-b-ca By the…