1 4 in the column space of -9 - 11 - 36 ? 3 2 12 O Yes O No 0 4 – 11 - 36 1 If "Yes," write as a linear combination of the columns of 9. | 3 2 12 1 4 36 %3D 3 2 12
1 4 in the column space of -9 - 11 - 36 ? 3 2 12 O Yes O No 0 4 – 11 - 36 1 If "Yes," write as a linear combination of the columns of 9. | 3 2 12 1 4 36 %3D 3 2 12
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Exercise on Column Spaces and Linear Combinations
**Question:**
Is the vector
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
\]
in the column space of the matrix
\[
\begin{bmatrix}
1 & 0 & 4 \\
-9 & -11 & -36 \\
3 & 2 & 12
\end{bmatrix}
\]?
- ○ Yes
- ○ No
**If "Yes," write**
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
\]
as a linear combination of the columns of
\[
\begin{bmatrix}
1 & 0 & 4 \\
-9 & -11 & -36 \\
3 & 2 & 12
\end{bmatrix}
\].
The solution should be in the form:
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
=
\begin{bmatrix}
1 \\
-9 \\
3
\end{bmatrix}
\cdot \_\_
+
\begin{bmatrix}
0 \\
-11 \\
2
\end{bmatrix}
\cdot \_\_
+
\begin{bmatrix}
4 \\
-36 \\
12
\end{bmatrix}
\cdot \_\_
\]
Fill in the blanks with appropriate scalars to express the given vector as a linear combination of the columns of the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5025798a-663c-4f82-a82a-d0677c58328a%2F5e5b47c6-b5bd-4de9-890f-c45ea0f3faa8%2F4kxb288_processed.png&w=3840&q=75)
Transcribed Image Text:### Exercise on Column Spaces and Linear Combinations
**Question:**
Is the vector
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
\]
in the column space of the matrix
\[
\begin{bmatrix}
1 & 0 & 4 \\
-9 & -11 & -36 \\
3 & 2 & 12
\end{bmatrix}
\]?
- ○ Yes
- ○ No
**If "Yes," write**
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
\]
as a linear combination of the columns of
\[
\begin{bmatrix}
1 & 0 & 4 \\
-9 & -11 & -36 \\
3 & 2 & 12
\end{bmatrix}
\].
The solution should be in the form:
\[
\begin{bmatrix}
0 \\
-6 \\
1
\end{bmatrix}
=
\begin{bmatrix}
1 \\
-9 \\
3
\end{bmatrix}
\cdot \_\_
+
\begin{bmatrix}
0 \\
-11 \\
2
\end{bmatrix}
\cdot \_\_
+
\begin{bmatrix}
4 \\
-36 \\
12
\end{bmatrix}
\cdot \_\_
\]
Fill in the blanks with appropriate scalars to express the given vector as a linear combination of the columns of the matrix.
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