n2 (n+ 1)2 (n+2)²] Let n be a positive integer. Let A, be the 3 x 3 matrix (n+1)² (n+2)² (n + 3)² |(n+2)² (n+3)² (n+4)²] 3. Show that the determinant of A, is –8. The whole point of Problem 3 is to show that you get the same answer no matter which n you use, expand all the quadratics inside the matrix, then use row operations to simplify the entries.

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A: To find the determinant of A=3601-231410-11-92-22

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Q: 6 2 2] 3 5 1 5 7 5. M = Transpose(M) = %3D (iii) [4 7 3 М — 8 5 2 Determinant(M) [4 6 3.

A: topic - matrices and determinants

Q: I need to prove each of the following, showing all steps.

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A:

Q: = 5.8. Let f₁(x) = x³ x² +1, f₂(x) = x³ + x² + x and f3 (x) = x³ + 2x²+3x+1 be three polynomials in…

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A: Explanation of the answer is as follows

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: 6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k…

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A: To find the determinant of matrix.

Q: Please avoid using chatgpt. Show the complete solution. Thank you!

A: YOUR  EXPLANATION

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

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Q: Find (3) BA + (4)AC, if possible что 2 O - 3] B=√₁ A.) (3) BA+ (Y)A(=[ A = -2 -3 3 O 1 O 1 -10 C =…

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Q: Suppose the only solution of AX-B is the zero matrix (A is nxn and B is nx1). Then the RREF of A | B…

A: Given the only solution of AX=B is the zero matrix ( A is nxn and B is nx1 ) . The RREF of A | B is…

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

A: