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E 3 9. If A= [1 10 16 -20 0-1 159 237 0 1 -431 0 0 1 0 0 determinant of A-74 +44 is, (A) 4 (C) 16 (A) λ, and λ₂ (C) λ, + A, and A, -A₂ 10. If the characteristic equation of a 2 x 2 matrix A is 2²-42 + 1 = 0, then the trace and determinant of A respectively are (A) -1 and 4 (C) 4 and 1 (D) 4 ; then the [100 (A) 0 1 0 001] 11. Ifà, and λ, are the eigenvalues of a 2 x 2 non-singular matrix A, then the eigenvalues of ad joint of A are (B) -4 (D) -16 300 (C) 0 3 0 0 03 (B) 1 and-4 (D) 4 and -1 (B) A and A (D) λ, x λ, and 12. If A is a 3 x 3 matrix with the characteristic equation A-SA²+2A-3=0, then 34-15A³ + 64¹ - 114 + 104-44¹ +104-204 +84-9/ is equal to (B) (D) 2₁ 2₂ [200] 020 002 40 040 004 3. Which of the following is NOT an eigenvector of the

E 3 9. If A= [1 10 16 -20 0-1 159 237 0 1 -431 0 0 1 0 0 determinant of A-74 +44 is, (A) 4 (C) 16 (A) λ, and λ₂ (C) λ, + A, and A, -A₂ 10. If the characteristic equation of a 2 x 2 matrix A is 2²-42 + 1 = 0, then the trace and determinant of A respectively are (A) -1 and 4 (C) 4 and 1 (D) 4 ; then the [100 (A) 0 1 0 001] 11. Ifà, and λ, are the eigenvalues of a 2 x 2 non-singular matrix A, then the eigenvalues of ad joint of A are (B) -4 (D) -16 300 (C) 0 3 0 0 03 (B) 1 and-4 (D) 4 and -1 (B) A and A (D) λ, x λ, and 12. If A is a 3 x 3 matrix with the characteristic equation A-SA²+2A-3=0, then 34-15A³ + 64¹ - 114 + 104-44¹ +104-204 +84-9/ is equal to (B) (D) 2₁ 2₂ [200] 020 002 40 040 004 3. Which of the following is NOT an eigenvector of the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please do all problems with just the letter choice 9 through 13 please 

X MInbox (13,580) - thomaskielbasins X 0(CR)%20(1).pdf Directions for questions 1 to 25: Select the correct alterna- tive from the given choices. is (A) 0 (C) 2 1. If A is a square matrix of order 5 with A = A' and non-negative determinant, then the determinant of A 02 CREATIVE WRITERS-contract fo X (A) 2. For two matrices A and B, if AB = A and BA - B, then which of the following statements is/are correct? I. A is an idempotent matrix. II. B is an idempotent matrix. (A) I only (B) II only (C) Both I and II (D) Neither I nor II 0 a-b bc-ac (C) 0 b-c ca-ab ab 1 a ca 3. Consider the matrix A=1 b C ab lowing is NOT equal to the determinant of A? 1 a a 1bb² C² 1 c (B) 1 (D) 5 (A) a nilpotent matrix (B) an idempotent matrix (C) an involutory matrix (D) None of these 6. The rank of the matrix P= 1 / 20 (B) (D) bc Which of the fol- 4. For a non-singular square matrix A, if A³ = A, then A must be a+bc a 1+a b+ca b 1+b c+ab c 1+c Search 1 a+la+a 1 b+1 b² +b 1 c+1 c²+c 5. If A is a matrix of order 6 x 9 with rank 5, then which of the following is true? (A) All the rows of A are linearly independent. (B) 5 columns of A are linearly independent. (C) AA is invertible. (D) ATA is invertible. 1 2 4 -3 2 -3 5 -4 13 -10 4 1 is 100% + 7. The value of x, in the solution of the system of linear equations x, + 2x₂ + 2x, = 4, 2x₁ - 2x, - x, = −3, 4x₁ + x₂ +2x, = 3 is- (A) 1 (C) 2 (A) 1 (C) 3 Untitled (4) 9. If A- 8. For a homogeneous system of linear equations AX = 0 with four equations in four unknowns, if the number of linearly independent solutions is one, then the rank of is. 1 10 16 -20 0-1 159 237 0 -431 0 1 0 0 0 1 determinant of 4°-74 +44 is (A) 4 (C) 16 (A) λ, and 2₂ (C) λ, + A, and 2, -2₂ (A) (C) (B) -1 (D) -2 10. If the characteristic equation of a 2 x 2 matrix A is 2²4λ + 1 = 0, then the trace and determinant of A respectively are (A) -1 and 4 (C) 4 and 1 100 010 0 1 0 (B) 2 (D) 4 ; then the 11. Ifà, and 2, are the eigenvalues of a 2 x 2 non-singular matrix 4, then the eigenvalues of ad joint of A are (B) -4 (D) -16 HH X 12. If A is a 3 x 3 matrix with the characteristic equation 2³-5λ² + 22 - 3 = 0, then 34° - 154 + 64¹ - 1146 + 104-44*+104-204² +84-91 is equal to (B) 1 and 4 (D) 4 and -1 (B) + (B) λ² and 2₂² 2₁ (D) , x A, and 2₂ 200 020 002 300 030 003 1 13. Which of the following is NOT an eigenvector of the 400 (D) 0 4 0 00 4
Transcribed Image Text:X MInbox (13,580) - thomaskielbasins X 0(CR)%20(1).pdf Directions for questions 1 to 25: Select the correct alterna- tive from the given choices. is (A) 0 (C) 2 1. If A is a square matrix of order 5 with A = A' and non-negative determinant, then the determinant of A 02 CREATIVE WRITERS-contract fo X (A) 2. For two matrices A and B, if AB = A and BA - B, then which of the following statements is/are correct? I. A is an idempotent matrix. II. B is an idempotent matrix. (A) I only (B) II only (C) Both I and II (D) Neither I nor II 0 a-b bc-ac (C) 0 b-c ca-ab ab 1 a ca 3. Consider the matrix A=1 b C ab lowing is NOT equal to the determinant of A? 1 a a 1bb² C² 1 c (B) 1 (D) 5 (A) a nilpotent matrix (B) an idempotent matrix (C) an involutory matrix (D) None of these 6. The rank of the matrix P= 1 / 20 (B) (D) bc Which of the fol- 4. For a non-singular square matrix A, if A³ = A, then A must be a+bc a 1+a b+ca b 1+b c+ab c 1+c Search 1 a+la+a 1 b+1 b² +b 1 c+1 c²+c 5. If A is a matrix of order 6 x 9 with rank 5, then which of the following is true? (A) All the rows of A are linearly independent. (B) 5 columns of A are linearly independent. (C) AA is invertible. (D) ATA is invertible. 1 2 4 -3 2 -3 5 -4 13 -10 4 1 is 100% + 7. The value of x, in the solution of the system of linear equations x, + 2x₂ + 2x, = 4, 2x₁ - 2x, - x, = −3, 4x₁ + x₂ +2x, = 3 is- (A) 1 (C) 2 (A) 1 (C) 3 Untitled (4) 9. If A- 8. For a homogeneous system of linear equations AX = 0 with four equations in four unknowns, if the number of linearly independent solutions is one, then the rank of is. 1 10 16 -20 0-1 159 237 0 -431 0 1 0 0 0 1 determinant of 4°-74 +44 is (A) 4 (C) 16 (A) λ, and 2₂ (C) λ, + A, and 2, -2₂ (A) (C) (B) -1 (D) -2 10. If the characteristic equation of a 2 x 2 matrix A is 2²4λ + 1 = 0, then the trace and determinant of A respectively are (A) -1 and 4 (C) 4 and 1 100 010 0 1 0 (B) 2 (D) 4 ; then the 11. Ifà, and 2, are the eigenvalues of a 2 x 2 non-singular matrix 4, then the eigenvalues of ad joint of A are (B) -4 (D) -16 HH X 12. If A is a 3 x 3 matrix with the characteristic equation 2³-5λ² + 22 - 3 = 0, then 34° - 154 + 64¹ - 1146 + 104-44*+104-204² +84-91 is equal to (B) 1 and 4 (D) 4 and -1 (B) + (B) λ² and 2₂² 2₁ (D) , x A, and 2₂ 200 020 002 300 030 003 1 13. Which of the following is NOT an eigenvector of the 400 (D) 0 4 0 00 4
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