1. Suppose A = [41] PAGE 7 (a) [1 Compute A², A³, and A4. Use these to conjecture a formula for A™ for any positive integer n. What is the matrix power A57 ? (b) [4

Q: If n is a positive integer, then [2 -168 -4 -2]^n  is [ ]  (Hint: Diagonalize the matrix first. Note…

A: Given that,  A=2-168-4-2 let A=21-84-2-1=2B Then An=2Bn                         1, where nis a…

Q: 4]         [8   7]      [7   2]             +               - [-4  6]         [8   8]      [3   4]…

A: Given expression is: 14−46+8788−7234

Q: 3) Consider the following matrix: A= 220 001 0 10 - 1 1 (i) Compute A™ ¹. (ii) Write A as a product…

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Q: 1. Consider the following matrices: (b) [2 0 1 -2 ------# C= 1 3 D= 3 2 0 -1 -1 (c) A = 53 Evaluate,…

A: Consider the following matrices.To evaluate the following:

Q: .

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Q: When reducing [A | I], a row in the A part consists of all zeros. What does this indicate about A-¹?…

A: We know that a matrix A is invertible if and only if A is non singular i.e. det(A)≠ 0

Q: -). Perform the following matrix multiplication: [5 2] 6 [1 2 12 -1 Lo 0 41 7 2. 7 1 4.

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Q: 10. Consider the following matrices: A = 13 0 1 3-5 1]. B A² BA CA DA 10-1 215 -3 4], C-[|-||---|| 0…

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Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

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Q: Which do you find easier? 3 1 (₁ - ( ) -- (3) (a) A = B = -1 1 1₁- (b) A = ()--(²3) B = -2 15 2 2-2

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Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: Consider the matrices [2 1 A = 2 2 -2 31 3271 and x = X1 B Xx2 a. Show that the equation Ax = x can…

A: TO solve the system of linear equation we use matrix method .

Q: 2. Use the scheme in Section 2.2 to find the inverse of the following matrix A. Recall that in that…

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Q: 3 5 (c) 4 2 -7

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Q: Calculate whether the given matrices are diagonalizable or not. That is, for each matrix, calculate…

A: We will use the fact if the eugen values of a matrix are distinct then the matrix is diagonalizable.

Q: n If A, B, and C are 2x2 matrices; and det(A) = 5, det(B) = 1, and det(C)=-4 then compute:…

A: Given A, B, C are 2x2 matrix. det(A)=5, det(B)=1 and det(C)=-4. We have to find, det2CTB2C-1ATC-1.

Q: 9. Show that the matrices ( ) ( ) (19). generate M₂×2(F). and (689)

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Q: Consider the matrix B given by where 2 3 23-3 3 -4 2 -1 0 0 det (A₁) + 4 - 3 5 -5 -4 . Then det (B)…

A: We find the determinant of a matrix by expanding with respect to any row or column. By taking sum of…