Problem 6: Given A, B E Maxn(R), which one of the following statements is false: A) If λ is an eigenvalue of A with associated eigenvector v then v is an eigenvector associated with the eigenvalue A². B) The determinant of A is always the product of its pivots. C) AB is orthogonal if A and B are both orthogonal matrices. D) The determinant of AB BA is 0. E) det A=0 if and only if rref(A) # In. Problem 7: If A is a 5 x 7 matrix with rank 3, which one of the following statements is true: A) The column space of A has dimension 2. B) The row space of A has dimension 4. C) The null space of A has dimension 4. D) Az = 0 has only the trivial solution. L E) A-¹ can be written as a multiplication of elementary matrices.
Problem 6: Given A, B E Maxn(R), which one of the following statements is false: A) If λ is an eigenvalue of A with associated eigenvector v then v is an eigenvector associated with the eigenvalue A². B) The determinant of A is always the product of its pivots. C) AB is orthogonal if A and B are both orthogonal matrices. D) The determinant of AB BA is 0. E) det A=0 if and only if rref(A) # In. Problem 7: If A is a 5 x 7 matrix with rank 3, which one of the following statements is true: A) The column space of A has dimension 2. B) The row space of A has dimension 4. C) The null space of A has dimension 4. D) Az = 0 has only the trivial solution. L E) A-¹ can be written as a multiplication of elementary matrices.
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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Transcribed Image Text:Problem 6:
Given A, B E Maxn(R), which one of the following statements is false:
A) If λ is an eigenvalue of A with associated eigenvector v then v is an eigenvector of A2,
associated with the eigenvalue A².
B) The determinant of A is always the product of its pivots.
C) AB is orthogonal if A and B are both orthogonal matrices.
D) The determinant of AB BA is 0.
E) det A = 0 if and only if rref(A) # In.
Problem 7:
If A is a 5 x 7 matrix with rank 3, which one of the following statements is true:
A) The column space of A has dimension 2.
B) The row space of A has dimension 4.
C) The null space of A has dimension 4.
D) Az = 0 has only the trivial solution.
E) A-¹ can be written as a multiplication of elementary matrices.
Problem 8:
Find the determinant of the matrix
A) (k-1)(k+2)
B) k
C) k-1
D) k + 2
E) 0
k k k
-1
-1 k
2
k
3
where k 0.
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