Notation: For a 3x3 matrix: • We will denote by m², the minor of order 2 obtained by deleting row i and column j. • We will denote by m; the minor of order 1 obtained by deleting every row but i and every column but j. • We will denote by pm? = m²; the principal minor of order 2 obtained by deleting row i and column i. • We will denote by pm = m; the principal minor of order 1 obtained by deleting every row by i and every column but i. • We will denote by 1pm the leading principal minor of order k. Calculate the following minors of A = -4 2 -5 -5 -5 1 5 -1 -2 (a) The minor of order 3 (b) The minor m3,2 of order 2 (c) The minor m of order 1 (d) The principal minor pm² of order 2 (e) The leading principal minor 1pm2 of order 2
Notation: For a 3x3 matrix: • We will denote by m², the minor of order 2 obtained by deleting row i and column j. • We will denote by m; the minor of order 1 obtained by deleting every row but i and every column but j. • We will denote by pm? = m²; the principal minor of order 2 obtained by deleting row i and column i. • We will denote by pm = m; the principal minor of order 1 obtained by deleting every row by i and every column but i. • We will denote by 1pm the leading principal minor of order k. Calculate the following minors of A = -4 2 -5 -5 -5 1 5 -1 -2 (a) The minor of order 3 (b) The minor m3,2 of order 2 (c) The minor m of order 1 (d) The principal minor pm² of order 2 (e) The leading principal minor 1pm2 of order 2
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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Transcribed Image Text:Notation: For a 3x3 matrix:
• We will denote by m², the minor of order 2 obtained by deleting row i and column j.
• We will denote by m; the minor of order 1 obtained by deleting every row but i and every column but j.
• We will denote by pm² = m², the principal minor of order 2 obtained by deleting row i and column i.
• We will denote by pm = m; the principal minor of order 1 obtained by deleting every row by i and every column but i.
• We will denote by 1pmk the leading principal minor of order k.
Calculate the following minors of A
=
−4 -5 -5
2
1
5
−5 -1
-2
(a) The minor of order 3
(b) The minor m32 of order 2
(c) The minor m₁ of order 1
(d) The principal minor pm² of order 2
(e) The leading principal minor 1pm2 of order 2
L
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