Q30E Give an example of a matrix聽A聽... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 3: Q30E (page 120)

Give an example of a matrixAsuch thatim(A)is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .

Short Answer

Expert verified

$[\begin{matrix} 1 \\ 5 \end{matrix}]$ is a matrix A such that im(A) is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .

Step by step solution

Consider the parameters.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

$i m a g e (f) = \{f (x) : x i n X\} = \{b i n Y : b = f (x), f o r s o m e x i n X\}$

The span of A is the collection of all products of the form Ab for some compatible column vector $b$ (i.e. b has as many elements as A has columns).

As $[\begin{matrix} 1 \\ 5 \end{matrix}]$ has only one column, thus, $[\begin{matrix} 1 \\ 5 \end{matrix}]$ is the matrix that is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .

Final answer.

$[\begin{matrix} 1 \\ 5 \end{matrix}]$ is a matrix A such that im(A) is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .

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91影视

Give an example of a matrixAsuch thatim(A)is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .

Short Answer

Step by step solution

Consider the parameters.

Final answer.

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91影视

Give an example of a matrixAsuch thatim(A)is spanned by the vector[15].

Short Answer

Step by step solution

Consider the parameters.

Final answer.

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Most popular questions from this chapter

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Give an example of a matrixAsuch thatim(A)is spanned by the vector $[\begin{matrix} 1 \\ 5 \end{matrix}]$ .