Enter T or F depending on whether the statement is true or false. Assume that matrices in the following statements are all square and of the same size. 1. If D1 and D2 are diagonal matrices, then D2D1=D1D2. 2. If L is a lower triangular matrix and D is a diagonal matrix, then LD=DL. 3. Every upper triangular matrix can be broken into the sum of a diagonal matrix and an upper triangular matrix that has all zeros on its diagonal. 4. If U1 and U2 are upper triangular matrices, then U2U1=U1U2. 5. Every invertible upper triangular matrix can be broken into the product of a diagonal matrix and an upper triangular matrix that has all ones on its diagonal.
Enter T or F depending on whether the statement is true or false. Assume that matrices in the following statements are all square and of the same size. 1. If D1 and D2 are diagonal matrices, then D2D1=D1D2. 2. If L is a lower triangular matrix and D is a diagonal matrix, then LD=DL. 3. Every upper triangular matrix can be broken into the sum of a diagonal matrix and an upper triangular matrix that has all zeros on its diagonal. 4. If U1 and U2 are upper triangular matrices, then U2U1=U1U2. 5. Every invertible upper triangular matrix can be broken into the product of a diagonal matrix and an upper triangular matrix that has all ones on its diagonal.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Enter T or F depending on whether the statement is true or false. Assume that matrices in the following statements are all square and of the same size.
1. If D1 and D2 are diagonal matrices, then D2D1=D1D2.
2. If L is a lower triangular matrix and D is a diagonal matrix, then LD=DL.
3. Every upper triangular matrix can be broken into the sum of a diagonal matrix and an upper triangular matrix that has all zeros on its diagonal.
4. If U1 and U2 are upper triangular matrices, then U2U1=U1U2.
5. Every invertible upper triangular matrix can be broken into the product of a diagonal matrix and an upper triangular matrix that has all ones on its diagonal.
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