4. Parts (a) and (b) are unrelated. (a) Suppose w is not a linear combination of vị, v2, and v3. Select the option that must be true about the vector equation T1v1 +x2V2 + x3V3 = w. (b) What is Span geometrically?

4. Parts (a) and (b) are unrelated. (a) Suppose w is not a linear combination of vị, v2, and v3. Select the option that must be true about the vector equation T1v1 +x2V2 + x3V3 = w. (b) What is Span geometrically?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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4. Parts (a) and (b) are unrelated.
(a) Suppose w is not a linear combination of vị, v2, and v3. Select the option that must be true about
the vector equation
T1v1 +x2V2 + x3V3 = w.
{000}
(b) What is Span
geometrically?
Answer (a) here: [Select ]
Answer (b) here: [Select]

Expert Solution

Step 1: Given.

Given: (a) $w$ is not a linear combination of $v_{1}, v_{2}$ and $v_{3}$ .

To find: (a) The option that must be true about the vector equation $x_{1} v_{1} + x_{2} v_{2} + x_{3} v_{3} = w$ .

(b) Geometrically, what is $Span \{(\begin{matrix} 0 \\ 1 \\ 0 \end{matrix}), (\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}), (\begin{matrix} 0 \\ - 1 \\ - 1 \end{matrix})\}$ ?

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