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Suppose is also an additive inverse of . Then
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Suppose is also an additive inverse of . Then
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Suppose is also an additive identity. Then
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Now add to both sides. Then .
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Therefore, from the uniqueness of the additive inverse proved in the above Problem addinvrstunique, it follows that .
Find the following if possible. If it is not possible explain why.
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Not possible
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Not possible
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Not possible
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Solution is: so the matrices are of the form
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Thus you must have . Therefore .
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Yes . Multiply on the left by .
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The reduced row echelon form is . There is no inverse.
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You need to show that acts like the inverse of because from uniqueness in the above problem, this will imply it is the inverse. From properties of the transpose, Hence and this last matrix exists.
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An factorization of the coefficient matrix is First solve which gives Then solve which says that and
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An factorization of the coefficient matrix is First solve which yields . Next solve This yields
These problems come from the end of Chapter 2 of Ken Kuttler’s A First Course in Linear Algebra. (CC-BY)
Ken Kuttler, A First Course in Linear Algebra, Lyryx 2017, Open Edition, pp. 90–98, 104–106.
2024-09-06 23:26:18