A. Construct a 2 × 2 matrix that is invertible but not diagonalizable. Also provide the inverse of your matrix. B. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

Q: Find the inverse of the matrix (if it exists).

A:

Q: If A is an 3× 4 matrix and the nullity of A equals 2, find the rank of A .

A:

Q: Find x such that the matrix is equal to its own inverse. A = -5 -6

A: Given A=6X-5-6

Q: Suppose A is an m x n matrix whose columns are linearly independent. What is the nullity of A?

A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: Find the inverse of the matrix (if it exists).

A:

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 10 -3 -6 -3…

A:

Q: Find the inverse of the matrix (if it exists).

A:

Q: Write down the necessary conditions for the matrix B2*2 (2 ∗ 2 matrix) to have an inverse matrix.

A: Necessary conditions for a 2*2 matrix to have an inverse matrix.

Q: Identify that the given matrix is Diagonalisable or not: -2 = | -2 6

A: A matrix is said to be diagonalizable if it is similar to a diagonal matrix. Also, if a matrix has…

Q: Find the inverse of the matrix if it exists.

A: Find the inverse of the matrix if it exists.     6-3-84

Q: Identify that the given matrix is Diagonalisable or not: -2 A = 2 6 -1 1 5.

A: It is diagonalisable

Q: 3 0 A =|-3 7] 1 -1 2 4 91

A:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given: -243-1

Q: Find the Inverse of Matrix (M).

A: We can compute inverse of matrix as follows

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) -4-2-4 3 1…

A: We first find the augmented matrix then by using elementary row operations, we find the inverse of…

Q: Find the inverse of cach matrix if possible. If a matrix is not invertible, explain why. 3 0 1 2 2…

A: Matrix A is invertible if and only if  following conditions hold: 1. A must be n×n square matrix…

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) -3 -2 -6 3…

A:

Q: Show that the matrix is not diagonalizable.

A:

Q: Find the inverse of the matrix (if it exists).

A: Now,

Q: Find the inverse of the matrix (if it exists).

A: Now determinant value is,

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: Decide whether the matrix -7 1 4 A = -12 1 8 -10 1 7, is diagonalizable over R. If it is,…

A: -714-1218-1017

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: Find the inverse of the matrix if it exists.

A: the given matrix is: 3-16-2 we have to find the inverse of the given matrix if it exists.

Q: Find x such that the matrix is equal to its own inverse. A = -3 -5 X = 6

A: Given,A = A-1AA-1=IAA = IA2 = IA = 5x-3-5

Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: Find the inverse of the given 3x3 matrix. By Gaussian elimination. -1] 0 1 1 -2 1 -1 0. 1.

A: We have to find the inverse of the matrix  12-1-2011-10  by Gaussian elimination.

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given: 1514

Q: Find the inverse of the given nonsingular matrix. -1 1. 2 -1 4. 3 0

A: Topic - inverse of matric

Q: If A is an invertible square matrix that is row equivalent to matrix B , then both A and B are row…

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: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 20 -6 -6 -3…

A: To Find: The inverse of the matrix(if it exists).  20-6-6-311-312

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A:

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) -5 3 -6 -2…

A:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A:

Q: Find x such that the matrix is equal to its own inverse.

A:

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

A:

Q: If A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent.

A: In A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent. You have 5 column…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: A=4-220

Q: The matrix A has the inverse. Answer yes or no

A:

Q: verify that the matrix B is the inverse of the matrix A. -1 A = B = -4 3 3. 2.

A: Note: You are allowed to ask 1 question at a time.

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: Find the inverse of the matrix A, if it exists. (If an inverse does not exist, enter DNE.) -3 A = 3…

A: We have to find the inverse of matrix

Q: Find the inverse of the matrix and verify that A-1 A = AA-1 =  I2 and B-1 B = BB-1 = I3.

A: see below the answer

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) -5 -2 -4 3…

A: To find the inverse of the matrix-5-2-4312625

Q: Give an example of  a matrix which is its own inverse ( that is , where A^-1=A)

A: We have to give an example of  a matrix which is its own inverse where A-1=A take A-1 on other…

Q: Find the inverse of the matrix.

A: A detailed solution is given below.

Q: Գ -1 - r] ]]

A: Given:      Matrix A=266276277  then  A-1=1A×AdjA          A=266276277…

Q: Find a non-zero 2 x 2 matrix such that -6 -8 30 40

A:

Q: Find the inverse of the matrix (if it exists).

A: given the matrix: 2-222