For what values of h are the vectors 1 1 1 2 2 h+1 linearly dependent? 1 3 4 h+2 " and h = −1 and h = 1 No such values for h. h = -1 8 h²-h+4] h can be any real numbers. 1 4
For what values of h are the vectors 1 1 1 2 2 h+1 linearly dependent? 1 3 4 h+2 " and h = −1 and h = 1 No such values for h. h = -1 8 h²-h+4] h can be any real numbers. 1 4
For what values of h are the vectors 1 1 1 2 2 h+1 linearly dependent? 1 3 4 h+2 " and h = −1 and h = 1 No such values for h. h = -1 8 h²-h+4] h can be any real numbers. 1 4
Solve this linear algebra multiple chhoice question, it deals with linear indepence and dependence.
Transcribed Image Text:**Question:**
For what values of \( h \) are the vectors
\[
\begin{bmatrix}
1 \\
1 \\
1 \\
h
\end{bmatrix},
\begin{bmatrix}
1 \\
2 \\
2 \\
h+1
\end{bmatrix},
\begin{bmatrix}
1 \\
3 \\
4 \\
h+2
\end{bmatrix},
\begin{bmatrix}
1 \\
4 \\
8 \\
h^2 - h+4
\end{bmatrix}
\]
linearly dependent?
**Options:**
1. \(\boxed{h = -1 \text{ and } h = 1}\)
2. No such values for \( h \).
3. \( h \) can be any real number.
4. \( h = -1 \)
5. \( h = 1 \)
**Answer:**
\[
\boxed{h = -1 \text{ and } h = 1}
\]
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![**Question:**
For what values of \( h \) are the vectors
\[
\begin{bmatrix}
1 \\
1 \\
1 \\
h
\end{bmatrix},
\begin{bmatrix}
1 \\
2 \\
2 \\
h+1
\end{bmatrix},
\begin{bmatrix}
1 \\
3 \\
4 \\
h+2
\end{bmatrix},
\begin{bmatrix}
1 \\
4 \\
8 \\
h^2 - h+4
\end{bmatrix}
\]
linearly dependent?
**Options:**
1. \(\boxed{h = -1 \text{ and } h = 1}\)
2. No such values for \( h \).
3. \( h \) can be any real number.
4. \( h = -1 \)
5. \( h = 1 \)
**Answer:**
\[
\boxed{h = -1 \text{ and } h = 1}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63690276-989f-4d64-8c21-2b5508217d3d%2F42ee5ddc-9a7f-494d-b67e-c6d874af2ca6%2Ft9dn66_processed.jpeg&w=3840&q=75)
