If there is a non-singular matrix P such as        P-1AP=D  , matrix A is called a diagonalizable matrix. A, n x n square matrix is ​​diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues ​​of the matrix A.   A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1     a)Write a program that calculates the eigenvalues ​​and eigenvectors of matrix A using NumPy.

Q: If there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A,…

A: import numpy as np m = np.array([[1,-1,-1],[1,3,1],[-3,1,-1]) print("Printing the Original square…

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Q: 43. For n > 2, the (i,j)-cofactor of an n x n matrix A equals (-1)i+j times the determinant of the…

A: Given: 43. Determine whether the statements are TRUE or FALSE. Write TRUE if the Statement is True…

Q: Consider the following. -4 2 0 1 -3 A = 0 4 P = 0 4 2 2 -1 1 2 2 (a) Verify that A is diagonalizable…

A: Answer: I have given answered in the handwritten format in brief explanation.

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Q: Let m > 4 be an integer and A be an m x (m– 1) matrix. If Rank(A) = 2, then the nullity of A is: %3D

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A:

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Q: xercises 1- If x= [1 4; 8 3], find: a) the inverse matrix of x. b) the diagonal of x. c) the sum of…

A: Code: x=[1 4;8 3]   %a in=inv(x)   %b di=diag(x)   %c sc=sum(x) s=sum(sc)   %d tr=x'

Q: 1 1 1. A =-1 1 det A = 1 7 6 5 4 6 5 4 3 A = 5 4 2. det A = 3. 2 4 3 2 1 1 2 0 3. If is A=3 4 0…

A: Below i have calculated first 3 PART.

Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not…

A: Answer :

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Q: summation of any matrix (a)?

A: Code: function sum_of_matrix= sum_element(a)[p,q]=size(a)sum_of_matrix=0;for i=1:p      for j=1:q…

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A: the answer is given below :

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A: Answer:

Q: Assume A is k x n-matrix and B is n x l-matrix and AB = 0. Prove that rank(A) + rank(B) < n.

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A: ANSWER:-

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A: Step 1  The answer is given in the below step

Q: Find the value of *a', if B = | is a singular matrix? (A) 5 9 (8) (C) 7 O B

A: Singular Matrix

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Q: ) Assume A is k × n-matrix and Q is n x n-invertible matrix. Prove that rank(AQ) = rank(A).

A: Solution:

Q: B) If x=[1 4; 8 3], y=[1 2] find : a) the inverse matrix of x. b) the diagonal of x. c) the sum of…

A: According to our guidelines, we can solve one question at a time. I solved B) here.Kindly, repost…

Q: Define the matrices: T [3 2; 0 -8; -4 3]; A = [diag(-1:2:3) T; -6 4 32 1]. Perform the following…

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A: I have answered this question in step 2.

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A:

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A: Adjacency matrix A:

Q: 33. If the product AB is defined and AB is a zero matrix, then either A or B is a zero matrix.

A: Given:   33. Determine whether the statement are TRUE or FALSE. Write TRUE if the Statement is True…

Q: 44. The determinant of an n x n matrix can be evaluated by a cofactor expansion along any row.

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A: Lets see the solution.

Q: Q3: 1- Give an example of symmetric matrix. 1 2 3 2- LET A =2 find AT and |A|. 1 3 1 2 13

A:

Q: Q1: if y = [1,2,3,4,6,5,4,3,8,9,7,6,5,4,3,2], then a) replace the first three elements of vector y…

A: The answer is as follows:-

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A: ANSWER:-

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A: we have to explain the question why it is true and false

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A:

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Q: Minimize the following minterms using K-MAP Y= m (0, 1, 2, 5, 13, 15 )

A: Given range 0-15 .  So 4 variable K map will be used.  To find? Minimized boolean function.

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Q: Illsutrate the Analysis of matrix multiply inner loops ?

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A: kindly upload remaining parts seperately.

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A: The data represents the labels of Graph The adjacency matrix represents the connected edges 1…