A square matrix is an upper triangular matrix if all elements below the principal diagonal are zero.
Question:
where a, b and d are real numbers. Discuss the validity of each of the following statements. If the statement is always true, explain why. If not, give examples.
(A) If A and B are 2 Ã 2 upper triangular matrix, then A + B is a 2 Ã 2 upper triangular matrix.
(B) If A and B are 2Ã2 upper triangular matrix, then A + B = B + A.
(C) If A and B are 2 Ã 2 upper triangular matrix, then AB is a 2 Ã 2 upper triangular matrix.
(D) If A and B are 2Ã2 upper triangular matrix, then AB = BA.
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Related Book For
College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
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