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Solved Problems for Chapter 4
Using only the properties given in Theorem th:propertiesofaddition and Theorem th:propertiesscalarmult, show that the additive
inverse of , , is unique.
Using only the properties given in Theorem th:propertiesofaddition and Theorem th:propertiesscalarmult, show that the zero
matrix, , is unique.
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Using only the properties given in Theorem th:propertiesofaddition and Theorem th:propertiesscalarmult, show that
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Using only the properties given in Theorem th:propertiesofaddition and Theorem th:propertiesscalarmult, as well as previous
problems, show
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Consider the matrices .
Find the following if possible. If it is not possible explain why.
- (a)
-
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- (b)
-
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- (c)
-
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- (d)
-
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- (e)
-
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- (f)
-
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Suppose and is an invertible matrix. Does it follow that Explain why or why
not.
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Show that if exists for an matrix, then it is unique. That is, if and then
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Find an factorization of the coefficient matrix and use it to solve the system of
equations.
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Find an factorization of the coefficient matrix and use it to solve the system of
equations.
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Bibliography
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