1 2 1 2 1 Let A = 4 03 Find: -2 30 2 1 2 6 1 (a) the nullspace (b) the nullity (c) the rank of the matrix A. (d) Then verify that rank(A)+nullity(A)= n where n is the number of column of A

Q: 1 4 2 3) Find the null space of the matrix A = |0 L-2 1 1 -1 -8 -4 -2

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Q: [2 3 Let A = and B = Find the (1,2)-entry of matrix X |3 5 given that XA+X=B. -3

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Q: [1 0 0 1 -2 2r – 4 |0 15. Consider the matrix A where r is a constant. | 1 -r + 2 The values ofr for…

A: This is a problem of Linear Transformation.

Q: 0 0 2 0 2 Q.5) Using Cayley-Hamilton theorem find A³ of the matrix A = 1 -3 5 2

A: Given: A=200120−352A3=?

Q: 1 1 2 2 2 2 5 5 |? A = the matrix 0 0 3 3 is the nullity of What Mustafa Furkan Ç Mustafa Furkan Ç…

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Q: 1 2 -1 2 -1 For what values of k will the matrix 3 be singular (singular = not invertible). -2 2 k

A: Ques 6 Let A=12-12-13-22k To find : value of k for which matrix A is singular. A matrix A is…

Q: 1 2 2 . For what value of a will the matrix A=| 2 а 1 2 а be singular? Explain.

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Q: 1 2 3 1 A = 1 0 1 -1 2 1 1 Find rank of the matrix

A: We have to find the rank of the given matrix…

Q: 3- -4 0 1 2 1 - Find the adjoint matrix adj(A). 0 -1 Let A = 3 1 -2 3 -1 -1 2 a) 1 b) -1 2 1 2 -1 0…

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Q: 1 -1 1 -1 1 3 -1 1 Let, A = -2 1 4 -1 3 3 -1 -5 1 -6, a. Find a 5x5 matrix B such that AB 0, where 0…

A: It is given a 4x5 matrix A In part (a) we can take the zero matrix B such that AB=0 as there is no…

Q: 6 1 0 0 2 2 10 1 (b) Let A Find the value of b for which the matrix A is singular.

A: Use the property of the singular matrix to determine the value of b. Also, singular matrices are…

Q: [1 0 [9 0 01 c) A-2 = |0 4 0 Lo o 1l 9. Find a matrix A that satisfies a) (3.4) =0 -1 1 |0 0 -1| 2.

A: ANSWER :

Q: (a) Let E1, E2 be n x n elementary matrices (n > 3) such that for any n x n matrix A E1A = Ap E2A =…

A: As per the guidelines of the company I am doing the 1st question with all sub-parts. Kindly repost…

Q: Find (a) the nullspace, (b) the nullity, and (c) the rank of the matrix A. Then verify that rank(A)…

A: Given: The matrix is given as follows, Here,

Q: 2 1 4 6 Find a matrix X that satisfies A(X+I,)=B, where A = and B = 6 5 3 5

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Q: Find (a) the nullspace, (b) the nullity, and (c) the rank of the matrix A. Then verify that rank(A)…

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Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

A: We have to determine u is in Col.E, the column space of E.

Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: 5. Consider the matrix -1 3 0 0 1 0 3 A = 1 (a) Find A-1, the inverse matrix of A by using your…

A: (a)       So substituting in equation (1), we get A-1=130310-631-51Therefore    A-1=0100-2113-5313

Q: -4 -3 31 -1 0. Find an invertible matrix Pand a diagonal matrix D such that D = P'AP. 6 -6 5 int)…

A: The given matrix,A=-4-330-10-6-65

Q: 5 7 2) 3 1and B -1-2 0 10 ( 5. The Matrix A and B are a non nxn matrix. Given that A= 2 11( %3D -5…

A: Given that A=572231-1-20 and B-1=100110-5-21 (a) The objective is to find A-1. Determinant of matrix…

Q: 2 3 3 Let A and B 3 5 given that AX+X=B. Find the (1,2)-entry of matrix X -3

A: Matrix multiplication, for matrix A and B can only be done if the number of columns of A is equal to…

Q: 1. Consider the matrix 1 1 3 1 1 -1 2 1 -2 4 1 6 2 -1 0 A = -3 1 3 (a) Find row space, R(A), and…

A: A transformation is called linearly independent when the nullity of the transformation is 0.…

Q: -5 41 ka) Find rank of matrix A 1 -2 1 -4 5. .

A: We are given a matrix 2-541-211-45 For checking the rank, first let us calculate the determinant of…

Q: 2 3 13 1 3 14 perform the indicated row operations. R₂-2R₁ R₂ ->>> 2 3 13 R₁ R₂ 1 3 14 14-16834-68…

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Q: -2 3 Find the dimension for the column space for the matrix, A = 1 3 0 0 0 0 None of these 3 4 206

A: The solution for the asked part is given as

Q: 0. 8. in the form A = EFGR where 7. Express the matrix A = 3 3 %3D 2 E,F, and G are elementary…

A: A matrix in row echelon form means that Gaussian elimination has been operated on the rows to form…

Q: [1 2 3 1 5 L5 6 0. Q3/: Consider the matrix A = 0 find A-1.

A: Given, A=123015560

Q: 1 0 2 2. Given the matrix. A = 2 -1 3 find A-, using the Gauss-Jordan method 4 1

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Q: -3 4 0 3 2 1 -1 3 о 1 -1 0 0 0 5 0 0 0 0 4 der the matrix A = 1 3 8. 1.

A: In this question, the following conditions are checked. Lower triangular matrix. Diagonalizable.…

Q: 2 0 O1: Let A = |B 3 1. Find the values of a and B for which A is 1 3 1. Non-singular. 2. SDD. 3.…

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Q: 0 2 1 2 4. Find the rank of the matrix N = 2 10 1 201 4

A: We have been given the matrix  Note - Since you have posted with multiple questions so, we will do…

Q: 0 1 ,then the matrix is 1 0 (a)positive definite (b) negative definite (c) -Tx] [j1. Q29. If A =

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) If T-1 -2] A = -2 2J' find all values of 2 for which the homogenous system (A1, - A)x=0 has a…

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Q: 2. The following matrices correspond to the augmented matrix of a linear system of equations. GIve…

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Q: 0 1] 1 by Gauss-Jordan elimination, let the augmented matrix 1 -1 2 While you are inverting the…

A: Let the given matrix be  A=1011111-12 To invert the matrix by Gauss -Jordan elimination method,…

Q: (b) The rank of the matrix A is 2. 2 4 2) A = (1 k 3 1 2 2/ (i) (ii) Determine the value of the…

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Q: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula 4 of…

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Q: a 2 0 Q1: Let A= B 3 1.Find the values of a and B for which A is 1 3 1. Non-singular. 2. SDD. 3. PD.…

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Q: 3. Let A be an invertible matrix such that A-¹ = NOT 2 0 1 2 01 1 1 Solve the system (2A2)x= b,…

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Q: A 10 x 16 matrix A has maximal rank. What is its nullity? а. 26 b. 16 с. 10 d. 6 е. О

A: Using Rank- Nullity Thereom,

Q: 9. Consider the matrix -- 1 A 2 2 -1 0 а. Write the equation det A = 0 in terms of x, y, and z. b.…

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Q: 1 1 1' Let A be a 3x3 diagonalizable matrix, P 1 1 p-1- 0 1 2. 0 0 -2 D 0. If P-'AP = D then A2 is…

A: I have explained all necessary information in the solution part

Q: 2. Using Gauss-Seidel, compute a solution to the problem Ax=b w matrix of the form 2 -1 0 0 -1. 2 -1…

A: Given Data: Let us consider the given matrix  A= 2 -1   0   0...........-1-1   2  -1…

Q: -30 3 -5 Let A = 97 -6 15 263 -24 43 Find an invertible matrix Q and an upper-triangular matrix T so…

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Q: 1. Consider the matrix 1 1 3 1 6. 2 -1 0 1 - A = 2 1 1 6 -3 -2 1 4 1 3 (a) Find row space, R(A), and…

A: A transformation is called linearly independent when the nullity of the transformation is 0.…

Q: -1 4 (1.1) Consider the matrix A = 1 What is the nullity of AT? 1 -4 -4 -8 (a) 0 (b) 1 (c) 2 (d) 3…

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Q: 1 1. Find numbers x, y and z such that the matrix A= 0 0 0 1 0 4 -2 A?+ satisfies 1 4 = 13 0.

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