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] 0 1 0 0 0 1 "Express without recurrence 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: Г1 1 17 0 1 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries. 3.
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] 0 1 0 0 0 1 "Express without recurrence 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: Г1 1 17 0 1 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries. 3.
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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![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]
0 1 0
0 0 1
"Express without recurrence
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:
Г1 1 17
0 1
0 0 1
1
Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ccaccca-775a-4ba1-9c6e-a3d8caea7c7f%2F99e9ae8d-121c-41be-b80b-276da0af7312%2Fi9ltaut_processed.png&w=3840&q=75)
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]
0 1 0
0 0 1
"Express without recurrence
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:
Г1 1 17
0 1
0 0 1
1
Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
3.
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