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Suppose that A is a 3x3 matrix whose determinant is 2. If B is obtained from A by exchanging row 1 with row 3, then det(B) If C' is obtained from A by multiplying the second row by 3, then det(C) = If D = 3A, then det(D)

Suppose that A is a 3x3 matrix whose determinant is 2. If B is obtained from A by exchanging row 1 with row 3, then det(B) If C' is obtained from A by multiplying the second row by 3, then det(C) = If D = 3A, then det(D)

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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Part I Suppose that A is a 3x3 matrix whose determinant is 2. If B is obtained from A by exchanging row 1 with row 3, then det(B) : If C is obtained from A by multiplying the second row by 3, then det(C) If D : 3A, then det (D) If the first two rows of E are the same as the first two rows of A, but the third row of E is equals to the sum of the first and third rows of A, then det (E) det (A") det (A¯') If F is a 3x3 matrix and all three rows of F' are the same, then det(F) = If G is obtained from A by subtracting 3 times the first row of A from the second row of A, and leaving the other rows unchanged, then det(G) = If H is a 3x3 triangular matrix whose diagonal entries are 3, -1 and -2, then det(H) det(I) If K is a square matrix that is not invertible, then det(K) = If L is the lower triangular matrix obtained from an LU decomposition of A, then det(L) If M BC, where B and C are as described above, then det(M) =
Transcribed Image Text:Part I Suppose that A is a 3x3 matrix whose determinant is 2. If B is obtained from A by exchanging row 1 with row 3, then det(B) : If C is obtained from A by multiplying the second row by 3, then det(C) If D : 3A, then det (D) If the first two rows of E are the same as the first two rows of A, but the third row of E is equals to the sum of the first and third rows of A, then det (E) det (A") det (A¯') If F is a 3x3 matrix and all three rows of F' are the same, then det(F) = If G is obtained from A by subtracting 3 times the first row of A from the second row of A, and leaving the other rows unchanged, then det(G) = If H is a 3x3 triangular matrix whose diagonal entries are 3, -1 and -2, then det(H) det(I) If K is a square matrix that is not invertible, then det(K) = If L is the lower triangular matrix obtained from an LU decomposition of A, then det(L) If M BC, where B and C are as described above, then det(M) =
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