Q44E Consider the plane 2x1鈭�3x2+4x3... [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: Q44E (page 160)

Consider the plane $2 x_{1} 鈭� 3 x_{2} + 4 x_{3} = 02 x_{1} 鈭� 3 x_{2} + 4 x_{3} = 0$ with basis $螔$ consisting of vectors $[\begin{matrix} 8 \\ 4 \\ 鈭� 1 \end{matrix}]$ and $[\begin{matrix} 5 \\ 2 \\ 鈭� 1 \end{matrix}]$ . If ${[{\overset{鈫�}{x}}_{螔}]}_{螔} = [\begin{matrix} 2 \\ 鈭� 1 \end{matrix}]$ , find $\overset{鈫�}{x}$ .

Short Answer

Expert verified

The $\overset{鈫�}{x}$ is equal to $[\begin{matrix} 11 \\ 6 \\ 鈭� 1 \end{matrix}]$ .

Step by step solution

Describe the coordinates in a subspace of ℝn

For a subspace with basis $螔$ as ${\overset{鈫�}{v}}_{1}, 鈥� {\overset{鈫�}{v}}_{2}, . .., {\overset{鈫�}{v}}_{n}$ then any vector $\overset{鈫�}{x}$ can be represented by $\overset{鈫�}{x} = c_{1} {\overset{鈫�}{v}}_{1} + c_{2} {\overset{鈫�}{v}}_{2} + . ..... + c_{n} {\overset{鈫�}{v}}_{n}$ and the basis coordinated vector is denoted by, ${[\overset{鈫�}{x}]}_{螔} = [\begin{matrix} c_{1} \\ c_{2} \\ 鈰� \\ c_{m} \end{matrix}]$

Find the x→

Determine the vector as $\overset{鈫�}{x}$ follows.

$\begin{matrix} \overset{鈫�}{x} = 2 [\begin{matrix} 8 \\ 4 \\ 鈭� 1 \end{matrix}] 鈭� 1 [\begin{matrix} 5 \\ 2 \\ 鈭� 1 \end{matrix}] \\ = [\begin{matrix} 16 \\ 8 \\ 鈭� 2 \end{matrix}] + [\begin{matrix} 鈭� 5 \\ 鈭� 2 \\ 1 \end{matrix}] \\ = [\begin{matrix} 11 \\ 6 \\ 鈭� 1 \end{matrix}] \end{matrix}$

Hence, the $\overset{鈫�}{x}$ is equal to $[\begin{matrix} 11 \\ 6 \\ 鈭� 1 \end{matrix}]$ .

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Short Answer

Step by step solution

Describe the coordinates in a subspace of ℝn

Find the x→

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91影视

Consider the plane 2x1鈭�3x2+4x3=02x1鈭�3x2+4x3=0with basis螔 consisting of vectors[84鈭�1] and [52鈭�1]. If [x鈫�螔]螔=[2鈭�1], findx鈫� .

Short Answer

Step by step solution

Describe the coordinates in a subspace of ℝn

Find the x→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Geometry

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.