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1 Solve the following systems of equations by Gauss-Jordan method. 1. 3x + 6 y 3z = -2, 6x + 6y + 3z-5, 2y + 3 = 1 2x+2y+z-w=-2, 2x+3y-2+2w=7,x+y+32-2w=-6₁ x+y+z+w=2. 2xy + 4z 12, 3x+2y+z= 10, x+y+z=6 3. 2x + y + z = 10, x + 4y + 92 = 16, 3x + 2y+32 = 18 [20]

1 Solve the following systems of equations by Gauss-Jordan method. 1. 3x + 6 y 3z = -2, 6x + 6y + 3z-5, 2y + 3 = 1 2x+2y+z-w=-2, 2x+3y-2+2w=7,x+y+32-2w=-6₁ x+y+z+w=2. 2xy + 4z 12, 3x+2y+z= 10, x+y+z=6 3. 2x + y + z = 10, x + 4y + 92 = 16, 3x + 2y+32 = 18 [20]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8BEXP
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21:45 ..ll l * Y 22.0 Vo a KB/S LTEE e46 54 tutorial_05_3110... Gauss Elimination method, Eigen values and Eigen vectors, Caley- Hamilton theorem, Diagonalization of a matrix 1 Solve the following systems of equations by Gauss-Jordan method. 1. 3x + 6 y – 3z = -2, 6x + 6y + 3z = 5, - 2y + 32 = 1 2 x+2y+z-w =-2, 2x + 3y – z+ 2w = 7. x+y+ 3z – 2w =- 6. x +y+z+w=2. 2r - v + 4: - 12, 3x + 21y + z - 10, x + v + z = 6 3. 2x + y + z = 10, x + 4y + 9z = 16, 3x + 2y + 3z = 18 4. 2 [2 07 Find the eigen values of A and A, where (i) A = 2 [1 2] (ii) 0 4 3 [8 -6 2 Find the eigen vectors of the matrix A - -6 7 -4 2 -4 3. 21 01 Obtain the eigen values and the corresponding eigen vectors for the matrix A = -1 0 1 0 0 1 [2 1 07 Determine the eigen roots of the matrix A = 0 2 1 0 0 2 |-1 1 If A- 2 -2 1 find eigen values of the following matrices -3 (1) A (ii) A? (iii) A (iv) AT (v) A + 21 (vi) A? + 3A + 21 Prepared by Dr. Atul Patel Science and Humanities Department LDCE, Ahmedabad Semester: I, Subject : Mathematics Tutorial: 05 bject Code: 3110014 Year: 2021 – ODD [1 -1 2 plete A - 2A + 4A° - 6A* + 2A³ + A? - 5A + I, where A = 0 2 0 1 1 -1 [3 07 he matrix A = diagonalizable ? Justify your answer. 1 3 9 Show that the following matrices are diagonalizable. Find also the modal and diagonal matrices. [2 2 -2] A - 0 3 0. Also find AS. 3 10 2 -1 -1 -1 2 -1 -1 Determine diagonal matrix orthogonally similar to the real symmetric matrix A = - 1 2
Transcribed Image Text:21:45 ..ll l * Y 22.0 Vo a KB/S LTEE e46 54 tutorial_05_3110... Gauss Elimination method, Eigen values and Eigen vectors, Caley- Hamilton theorem, Diagonalization of a matrix 1 Solve the following systems of equations by Gauss-Jordan method. 1. 3x + 6 y – 3z = -2, 6x + 6y + 3z = 5, - 2y + 32 = 1 2 x+2y+z-w =-2, 2x + 3y – z+ 2w = 7. x+y+ 3z – 2w =- 6. x +y+z+w=2. 2r - v + 4: - 12, 3x + 21y + z - 10, x + v + z = 6 3. 2x + y + z = 10, x + 4y + 9z = 16, 3x + 2y + 3z = 18 4. 2 [2 07 Find the eigen values of A and A, where (i) A = 2 [1 2] (ii) 0 4 3 [8 -6 2 Find the eigen vectors of the matrix A - -6 7 -4 2 -4 3. 21 01 Obtain the eigen values and the corresponding eigen vectors for the matrix A = -1 0 1 0 0 1 [2 1 07 Determine the eigen roots of the matrix A = 0 2 1 0 0 2 |-1 1 If A- 2 -2 1 find eigen values of the following matrices -3 (1) A (ii) A? (iii) A (iv) AT (v) A + 21 (vi) A? + 3A + 21 Prepared by Dr. Atul Patel Science and Humanities Department LDCE, Ahmedabad Semester: I, Subject : Mathematics Tutorial: 05 bject Code: 3110014 Year: 2021 – ODD [1 -1 2 plete A - 2A + 4A° - 6A* + 2A³ + A? - 5A + I, where A = 0 2 0 1 1 -1 [3 07 he matrix A = diagonalizable ? Justify your answer. 1 3 9 Show that the following matrices are diagonalizable. Find also the modal and diagonal matrices. [2 2 -2] A - 0 3 0. Also find AS. 3 10 2 -1 -1 -1 2 -1 -1 Determine diagonal matrix orthogonally similar to the real symmetric matrix A = - 1 2
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