1. Determine whether the following statements are True or False. Explain. (a) The row echelon form of a matrix is unique. (b) A system of 5 linear equations with 6 unknowns can have a unique solution. (c) Every homogenous system has at least one solution. (d) If A and B are two n n matrices then (A + B)2 = A2 + 2AB + B2: (e) If A and B are square matrices of the same size such that det(A) = det(B) then det(A+ B) = 2 det(A): (f) If A is a n n matrix then reduced row echelon form of A is In: (g) If A is an invertible matrix then adj(A) is also invertible matrix.
1. Determine whether the following statements are True or False. Explain. (a) The row echelon form of a matrix is unique. (b) A system of 5 linear equations with 6 unknowns can have a unique solution. (c) Every homogenous system has at least one solution. (d) If A and B are two n n matrices then (A + B)2 = A2 + 2AB + B2: (e) If A and B are square matrices of the same size such that det(A) = det(B) then det(A+ B) = 2 det(A): (f) If A is a n n matrix then reduced row echelon form of A is In: (g) If A is an invertible matrix then adj(A) is also invertible matrix.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Determine whether the following statements are True or False. Explain.
(a) The row echelon form of a matrix is unique.
(b) A system of 5 linear equations with 6 unknowns can have a unique solution.
(c) Every homogenous system has at least one solution.
(d) If A and B are two n n matrices then (A + B)2 = A2 + 2AB + B2:
(e) If A and B are square matrices of the same size such that det(A) = det(B) then det(A+
B) = 2 det(A):
(f) If A is a n n matrix then reduced row echelon form of A is In:
(g) If A is an invertible matrix then adj(A) is also invertible matrix.
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