(a) Write an example for an Involuntory Matrix A, and hence evaluate 3A6 – 2Aª – A²

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

A:

Q: ix A, find (if possible) a nonsingular matrix P such that P-AP -3 0 0. 15-4 4 0 5

A: Introduction: A square matrix A is diagonalizable in linear algebra if it is similar to a diagonal…

Q: Find a matrix P that diagonalizes A, and check your work by computing P-1AP. -2 A = | 0 3 3

A:

Q: Give an example of a 3 x 3 skew-symmetric matrix A that is not diagonal. A =

A:

Q: (c) A = 1 B =

A:

Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

A:

Q: (d) Let C be an nXn matrix. Explain why if the echelon form of C has at least one zero row, then C…

A: To prove, if matrix C has at least one zero row then the matrix is not invertible.

Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

A: Given:

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. 'n' O True O False

A:

Q: Determine the dimension of the matrix. -3 7 15 0 5 0 3 3 4 1 67

A: It is required to find the dimensions of the given matrices.

Q: eat) -1 = et) where A is a real matrix of class nxn . Error true

A: Given that, e^at-1=e^t where A is the real matrix of class n×n.

Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: Find x such that the matrix A is nonsingular.

A: Matrix A is said to be non singular if the determinant value is non zero.

Q: (b). Find out the similar matrix of given matrix:

A: Similar Matrices: Ant two matrices A and B are said to be similar if there exists an invertible…

Q: For a square matrix A, AAT = AT A. A True В False

A:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

A:

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

A:

Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: 9. Solve the matrix equation C-A(X B) = D for X. Note that A, B, C, D, and X are all n x n…

A:

Q: Consider the multiplication AB is existing with the size (M × N) , where B is a matrix of size (L ×…

A: Consider the given information. The multiplication of two matrix is possible if and only if the…

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: If A is a skew symmetric matrix, what type of matrix is A T ? Justify your answer.

A: Given: A is a skew-symmetric matrix.

Q: Diaganolize the following matrix. 0 0 -1 -1 0 0 3

A:

Q: Diaganolize the following matrix. 1 0 6 -1 0 O 0 0] P D = P-1

A: Calculating eigen values and eigen vectors For eigen values 4-λ-106-1-λ000-λ =0 -λ(λ-2)(λ-1)=0 λ1=2…

Q: Find a formula in terms of k for the entries of A", where A is the diagonalizable matrix below. 4 -2…

A:

Q: Consider the following matrix: -31 A = -3 -4 9. 1 -2 (a) Verify that A is diagonalizable. (b) Find…

A: Since it is multiple questions with multipart, as per our company guidelines we have to solve the…

Q: Q1: Find a matrix P that diagonalizes A , and check your work by computing P-'AP ; [2 0 -2 1) 4 = %…

A:

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: True or False? Suppose that A is any n x m or n xn matrix, then the matrix A'A will be the transpose…

A:

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: The row space of a matrix equals its column space. O True O False

A: Let the matrix Amxn having m rows and n columns. If the matrix has rank r after reduced Echelon…

Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is…

A:

Q: If A is a skew symmetric matrix, what type of matrix is AT ? Justify your answer.

A: If A is a skew symmetric matrix, then our aim is to tell the type of AT matrix?

Q: Let A be an invertible, n x n matrix such that A² = A. a) Calculate det(A). b) If n = 3, what is A?…

A:

Q: - Which of the following operations can we perform for a matrix A of any dimension? (i) A + A (ii)…

A:

Q: Drow the digraph represented by the adjacency matrix 1 ㅇ 1 0- ㅇ ㅇ 1 ㅇ 1 ㅇ ㅇ 1 1 0 0 0 10 0 0 1 0 0 0…

A:

Q: For a square matrix A, AAT = ATA. %3D A) True False

A: We have to find the given statement is true or false.

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A:

Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 1, a22 = 5, a33 = 4, a12 = 3, a13 = 2, and =…

A: Given A is 3×3 Symmetric matrix with entries a11=1 , a22=5 , a33=4 , a12=3a13=2 and a32=0.We know…

Q: Give an example of a 4 by 4 matrix A, which is not symmetric, however A is symmetric.

A: A square matrix is said to be symmetric if it is symmetric about the main diagonal.

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: Use the following matrix. A = -1 −2 0 3 2 1 5 2 1 What is the sum of matrix A and its…

A: Given, A=-1-20321521

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5x5)) =

A:

Q: Find the LU- Factorization of the matrix A below 1 -2 3 A = 2 1 -4 4 1-4 6. 5 -2

A: Given 21-1-20321-441-465-2

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

A:

Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

A:

Q: Consider an n x p matrix A and a p x m matrix B. If ker(A)-im(B), what can you say about the produet…

A:

Q: O Prove that if a matrix A satisfies A² = A, then I — 2A = (I — 2A)−¹.

A:

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.