(b) If A and B are square matrices of the same size, then det (A + B) = det (A)+det(B).

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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Un please do PART B linear alg

State, with a brief explanation, whether the following propositions are
Problem 1.
true or false.
(a) If A and B are nxn matrices with no zero entries, then AB # Onxn.
(b) If A and B are square matrices of the same size, then det(A + B) = det (A)+det(B).
(c) The set
{][+][]}
4
5
is a linearly independent subset of R³.
6
8
0
x 2
(d) T: R³ R4, defined by T
([:])
is a linear transformation.
2
2x + 1
3y - 2
(e) Two different matrices may have the same eigenvalues.
Transcribed Image Text:State, with a brief explanation, whether the following propositions are Problem 1. true or false. (a) If A and B are nxn matrices with no zero entries, then AB # Onxn. (b) If A and B are square matrices of the same size, then det(A + B) = det (A)+det(B). (c) The set {][+][]} 4 5 is a linearly independent subset of R³. 6 8 0 x 2 (d) T: R³ R4, defined by T ([:]) is a linear transformation. 2 2x + 1 3y - 2 (e) Two different matrices may have the same eigenvalues.
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