**Problem 8** Let \[ A = \begin{pmatrix} 3 & 12 & 3 \\ 3 & 12 & 3 \\ 7 & -1 & 2 \end{pmatrix} \] (i) Determine if \( A \) is diagonalizable, and if it is, determine the matrices \( P \) and \( D \) such that \( A = PDP^{-1} \). (ii) Compute \( A^{12} \).

Q: If any three square matrices have the same size as A ,B,C AB=I and CA=I prove that A=C=A^-1

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Q: Also, how is the second to last 4x4 matrix on the last page is found?

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Q: A matrix is called skew-symmetric if A^T = −A. If A is a n × n matrix, then show the following: i.…

A: Solution:Given: is any matrixwe have to show that(i). The matrix is symmetric(ii). The matrix is…

Q: Calculate A^-1 and use it to solve the matrix equations 1 12 5 12 ²2). 5 = ( − 3), 5₂ = ( ¹3 ). -5 A…

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Q: 7. - B-[73] Solve for X in the matrix equation: B-4X = A 6

A: Given:  A=1-6510B=-237-1 to solve for X in the matrix equation: B-4X=A

Q: Let A, B, C be invertible n x n matrices. SOLVE for A in: A^-1B^-1 = C^-1

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Q: Solve the matrix equation AX = B, where -1 하 A: 1 and B 1 1 [6] 0 1 =

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Q: Find a real matrix A such that A ^6 = (09, -90)

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Q: t A be the square matrix (abcd) A. If ad−bc = 1, then show that A^−1 =(d−b−ca ) B. If ad−bc=α, then…

A: If  is a square matrix then its inverse is where

Q: How can I prove that a 4x4 matrix is invertible. Also how can I write that matrix as a product of…

A: The objective of this question is to determine if a given 4x4 matrix is invertible and if so, to…

Q: solve for x and y in the matrix A= [ x -4 3 y] if A^2 = [52 -36  27  -11] x = y =

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Q: Which (if any) columns of B may be individually deleted to leave a 4 by 4 matrix whose columns span…

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Q: Given the matrices A and B, solve for X. 5X - B = A. 5 A: - [31]-[9] = and B = -4 Select one: a. O…

A: A = -35-3   -4   ,   B = -3  4-355X-B = A

Q: Solve for x and y in the matrix A=[x 3 2 y] if A^2 = [ 31 12 8 87] x = y =

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Q: Suppose A, B, and X are n x n matricies with A, X, and A - AX invertible and suppose (A - AX)^-1 =…

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Q: Show that if A is a square matrix that satisfies the equation 2 A²-A-I-O, then its inverse is A-¹ =…

A: A square matrix M is said to be invertible if det(M)≠0 . If M is invertible,  then MM-1=I=M-1M ,…

Q: Find the matrix A (in terms of B, C, and D) if (4DA-'B )-1 = C

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Q: A and B are n x n matrices.    check the true statements below:   1) det(A)det(B) = -det(B^(t)A^(t))…

A: The objective of the question is to verify the truthfulness of two statements related to the…

Q: for part b), how can you multiply the E1^-1 and A as they are not the same size matrix? is that…

A: Given that encryption matrix A is of size 2 x 4.   Now, from rule of multiplication of matrices in…

Q: Suppose matrix A is 6×8. Describe (using appropriate terminology) how you would determine whether…

A: It is given that, the order of the given matrix A is 6*8.

Q: Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many…

A: Given: The trace of a matrix is equal to 10 and the matrix is an identity matrix.   To determine:…

Q: a+4b-2c=0 -2a-6b+5c=5 3a+14b-4c=8 use inverse matrix to solve and find a^-1

A: a+4b-2c=0 -2a-6b+5c=5 3a+14b-4c=8 use inverse matrix to solve and find a^-1 We shall solve this…

Q: What 3 x 3 elimination matrix replaces row 3 by row 3 minus 4 times row 2?

A: Consider a general 3x3 matrix as shown belowA=abcdefghi→Row 1 R1    →Row 2 R2    → Row 3 R3

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.