Consider the following statements: I. det(A" B) =det (B" A) detC II. If A, B, C are square invertible matrices of the same size, then det(A" B-!CA-!) = det B III. If A and B are two 4 × 4 matrices such that AB = 0, then either A or B is a zero matrix IV. If the augmented matrix [A : b] of the linear system Ax = b is reduced to a reduced row echelon form, then the system is consistent V. For the matrix A, the equality A²? = A is satisfied only for A = I or A = 0 How many of the above statements must always be true? (i) 1 (ii) 2 (iii) 3 (iv) 4 (v) 5 Mark the correct answer in ois
Consider the following statements: I. det(A" B) =det (B" A) detC II. If A, B, C are square invertible matrices of the same size, then det(A" B-!CA-!) = det B III. If A and B are two 4 × 4 matrices such that AB = 0, then either A or B is a zero matrix IV. If the augmented matrix [A : b] of the linear system Ax = b is reduced to a reduced row echelon form, then the system is consistent V. For the matrix A, the equality A²? = A is satisfied only for A = I or A = 0 How many of the above statements must always be true? (i) 1 (ii) 2 (iii) 3 (iv) 4 (v) 5 Mark the correct answer in ois
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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![Consider the following statements:
I. det(A" B) =det (B" A)
II. If A, B, C are square invertible matrices of the same size, then det(A" B-\CA-!) =
detC
det B
III. If A and B are two 4 × 4 matrices such that AB = 0, then either A or B is a zero matrix
IV. If the augmented matrix [A : 6] of the linear system Ar = b is reduced to a reduced row
echelon form, then the system is consistent
V. For the matrix A, the equality A² = A is satisfied only for A = I or A = 0
How many of the above statements must always be true?
(i) 1
(ii) 2
(iii) 3
(iv) 4
(v) 5
Mark the correct answer in ois](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52974ece-88de-4679-ac9c-318cece213a0%2F60e055af-1687-447b-a819-df11f3be57e8%2Flohsey_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following statements:
I. det(A" B) =det (B" A)
II. If A, B, C are square invertible matrices of the same size, then det(A" B-\CA-!) =
detC
det B
III. If A and B are two 4 × 4 matrices such that AB = 0, then either A or B is a zero matrix
IV. If the augmented matrix [A : 6] of the linear system Ar = b is reduced to a reduced row
echelon form, then the system is consistent
V. For the matrix A, the equality A² = A is satisfied only for A = I or A = 0
How many of the above statements must always be true?
(i) 1
(ii) 2
(iii) 3
(iv) 4
(v) 5
Mark the correct answer in ois
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