(a) Show that if A has the repeated eigenvalue 1 with two linearly independent associated eigenvectors, then every nonzero vector v is an eigenvector of A. (Hint: Express v as a linear combination of the linearly independent eigen- vectors and multiply both sides by A.) (b) Conclude that A must be given by Eq. (22). (Suggestion: In the equation Av = Av take v = [1 0]' and v = [0 1]'.)

Q: e. Determine whether the rows of A are linearly independent. f. Let the columns of A be denoted by…

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Q: Perform the following operation: 1- -5 4 3] a +a 3 1 4 -a ||

A: Given that we have to the find the product of given matrix

Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: The dimension of the row-space of a matrix equals the number of rows of the matrix. Select one: O…

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Q: A = 1 0 1 2 1 41-2 34 2 2 1 -1 2 21 -1. LO 10

A: The solution is given as

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: The product of a 5 ´ 3 matrix and a 3 ´ 5 matrix is

A: When we do matrix multiplication: The number of columns of the 1st matrix must equal the number of…

Q: 6 -2 0 1 4 1 0 4 4 3 -1 -1 2 0 5 A 5 ||

A: The solution is given as

Q: 1 2 C= 1 A = 1 -2 3 D = 1 1 1 -1 1 -1 -9 B = 1 1 1 1 2 -1 -1 4 1 find the matrix 2A – 3B + C. Do…

A: Given A = 11-2110B = 11-1111C = 1232-11D = 1-1-9-141

Q: Solve for the 2 x 2 matrix X: X + 2 23 5 3 X.

A: Introduction: A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for…

Q: Find the power of A for the matrixA16

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Q: The product of a 2 ´ 3 matrix and a 3 ´ 2 matrix is

A: When we do multiplication: The number of columns of the 1st matrix must equal the number of rows…

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: = [2 1 3 -1 -1 -1 2

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Q: Give an example example of a 3x5 matrix in BREF where RX=0 has unique solution.

A: The aim is to find an example of  matrix in RREF where  has a unique solution.

Q: Write an augmented matrix for the follo 6x - 5y +z = -9 8x - 7y +z = 7 9y-2z = - 2 %3D %3D

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Q: -x+2y-2z 5 3x-3y+5z = -6 -2x+3y-4z 6 Write the augmented matrix:

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Q: Consider the matrix product: 2 3. -3 -1 -2 1 H = -2 -1 1 -3 2 -1 0 %3D 0 2 -1 -1 1 2

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

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