Q3.1-16E For each matrix聽A in Exercise 1... [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: Q3.1-16E (page 119)

For each matrix $A$ in Exercise 14 through 16, find vectors that span the image of $A$ . Give as few vectors as possible. Use paper and pencil.
$A = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{matrix}]$

Short Answer

Expert verified

Thus, the resulting vector that span the image of $A$ is $[\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}] a n d [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$ .

Step by step solution

Span of the given matrix.

The given matrix is: $A = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{matrix}]$

The above matrix represents a linear transformation form $T : i^{2} 鈫� i^{4}$ and defined as $T (x) = A x$ .

The objective is to obtain the vectors that span the image of localid="1664173607564" $A$ .

The column vectors of $A$ is solved as follows:

$u_{1} = [\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}], u_{2} = [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$

The column vectors are span the image of A.

Possible set of vectors.

Let $x = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]$ then the equation solve as follows:

$T (x) = A x = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = x_{1} [\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}] + x_{2} [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$

Therefore, the resulting vector that span the image of $A$ is $[\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}]$ and $[\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$ .

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91影视

For each matrix $A$ in Exercise 14 through 16, find vectors that span the image of $A$ . Give as few vectors as possible. Use paper and pencil.
$A = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{matrix}]$

Short Answer

Step by step solution

Span of the given matrix.

Possible set of vectors.

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91影视

For each matrixA in Exercise 14 through 16, find vectors that span the image of A. Give as few vectors as possible. Use paper and pencil.A=[11121314]

Short Answer

Step by step solution

Span of the given matrix.

Possible set of vectors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For each matrix $A$ in Exercise 14 through 16, find vectors that span the image of $A$ . Give as few vectors as possible. Use paper and pencil.
$A = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \end{matrix}]$