1. (15 pts) Determine if the following statements are true or false. If true, justify why...
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1. (15 pts) Determine if the following statements are true or false. If true, justify why the statement is true (don't just give one example). If false, give a counterexample. Any answer that just states "True" or "False" will result in this exam being marked "Incomplete." (a) Suppose A: R² → R², B : R² → R², and A ‡ B. Suppose also that A rotates vectors by 0₁ counterclockwise about the origin, and A rotates vectors by 2 counterclockwise about the origin. Then A and B commute. (b) [-a, a] is a subspace of R. (c) Elementary matrices perform elementary row operations on a square matrix A when multiplied on the left or on the right of matrix A. (d) A left inverse of an element a of a set S under multiplication is an element of S that when multiplied on the left of a, the resulting product is the identity element (i.e. a ¹.a = id). Every mxn matrix that can be row reduced to (Im|0), where 0 is an mx(nm) submatrix containing only zeros. (e) The the set of all integrable functions forms a vectorspace. 1. (15 pts) Determine if the following statements are true or false. If true, justify why the statement is true (don't just give one example). If false, give a counterexample. Any answer that just states "True" or "False" will result in this exam being marked "Incomplete." (a) Suppose A: R² → R², B : R² → R², and A ‡ B. Suppose also that A rotates vectors by 0₁ counterclockwise about the origin, and A rotates vectors by 2 counterclockwise about the origin. Then A and B commute. (b) [-a, a] is a subspace of R. (c) Elementary matrices perform elementary row operations on a square matrix A when multiplied on the left or on the right of matrix A. (d) A left inverse of an element a of a set S under multiplication is an element of S that when multiplied on the left of a, the resulting product is the identity element (i.e. a ¹.a = id). Every mxn matrix that can be row reduced to (Im|0), where 0 is an mx(nm) submatrix containing only zeros. (e) The the set of all integrable functions forms a vectorspace.
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Hospitality Financial Accounting
ISBN: 978-0470083604
2nd Edition
Authors: Jerry J. Weygandt, Donald E. Kieso, Paul D. Kimmel, Agnes L.
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