? ? ? ? ? V 1. Different sequences of row operations can lead to different echelon forms for the same matrix. V V V 2. The linear system Ax = b will have a solution for all b in R" as long as the columns of the matrix A do not include the zero column. 3. If A is a square matrix satisfying A² = 0 (where O is the zero matrix), then A + I is invertible. 4. If a linear system has the same number of equations and variables, then it must have a unique solution. ✓ 5. If all the diagonal entries of a square matrix are zero, the matrix is not invertible.
? ? ? ? ? V 1. Different sequences of row operations can lead to different echelon forms for the same matrix. V V V 2. The linear system Ax = b will have a solution for all b in R" as long as the columns of the matrix A do not include the zero column. 3. If A is a square matrix satisfying A² = 0 (where O is the zero matrix), then A + I is invertible. 4. If a linear system has the same number of equations and variables, then it must have a unique solution. ✓ 5. If all the diagonal entries of a square matrix are zero, the matrix is not invertible.
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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V 1. Different sequences of row operations can lead to different echelon forms for the same matrix.
V
V
V
2. The linear system Ax = b will have a solution for all b in R" as long as the columns of the matrix A do not include the zero column.
3. If A is a square matrix satisfying A² = 0 (where O is the zero matrix), then A + I is invertible.
4. If a linear system has the same number of equations and variables, then it must have a unique solution.
✓ 5. If all the diagonal entries of a square matrix are zero, the matrix is not invertible.
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