Note that the only entry in a 1 x 1 matrix is on the diagonal. The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example, in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0: 1 1 0 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
Note that the only entry in a 1 x 1 matrix is on the diagonal. The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example, in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0: 1 1 0 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Note that the only entry in a 1 x 1 matrix is on the diagonal.
The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example,
in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0:
1 1
0 1
0 0 1
Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
Transcribed Image Text:The diagonal of a square matrix refers to all elements in a line from the top-left to the bottom-
right of the matrix. For example, in the 3 x 3 matrix below, all diagonal entries are 1 where
off-diagonal entries are 0:
[1 0 0
1
0 0
1
"Express without recurrence
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