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Linear Algebra
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1. Vectors
2. Matrices
3. Linear equations
System of linear equationsGaussian EliminationPivot positions and columnslockLinear dependence and independencelockElementary matriceslockLinear transformationlock
4. Matrix determinant
IntroductionDeterminant of elementary matricesInvertibility, multiplicative and transpose properties of determinantslockLaplace expansion theoremlockCramer's rule and finding inverse matrix using determinantslockGeometric interpretationlock
5. Vector space
SubspaceRelationship between pivots and linear dependenceSpanning Set of a vector spacelockBasis vectorslockConstructing a basis for a vector spacelockNull spacelockColumn spacelockRank and nullitylock
6. Special matrices
7. Eigenvalues and Eigenvectors
IntroductionBasic propertiesEigenspace and eigenbasislockSimilar matriceslockDiagonalizationlockAlgebraic and geometric multiplicitylock
8. Orthogonality
Orthogonal projectionsOrthonormal sets and basesOrthogonal complementlockOrthogonal matriceslockLeast squareslockGram-Schmidt processlock
9. Matrix decomposition
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Problem set - Introduction to Vectors (Linear Algebra)
schedule Dec 30, 2023
Last updated local_offer
Tags Linear Algebra
tocTable of Contents
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Compute the following:
$$2
\begin{pmatrix}
3\\1
\end{pmatrix}$$
Your answer
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Multiply each component by the scalar constant like so:
$$2\begin{pmatrix}
3\\1
\end{pmatrix}=
\begin{pmatrix}
2\times3\\2\times1
\end{pmatrix}=
\begin{pmatrix}
6\\2
\end{pmatrix}$$
Compute the following:
$$\begin{pmatrix}
2\\3
\end{pmatrix}+
\begin{pmatrix}
1\\-1
\end{pmatrix}$$
Your answer
Submit answer
Show solution
To add two vectors, add each pair of components like so:
$$\begin{pmatrix}
2\\3
\end{pmatrix}+
\begin{pmatrix}
1\\-1
\end{pmatrix}=
\begin{pmatrix}
3\\2
\end{pmatrix}$$
Compute the following:
$$\begin{pmatrix}
1\\4
\end{pmatrix}-
\begin{pmatrix}
1\\-1
\end{pmatrix}$$
Your answer
Submit answer
Show solution
To subtract two vectors, perform the subtraction for each pair of components like so:
$$\begin{pmatrix}
1\\4
\end{pmatrix}-
\begin{pmatrix}
1\\-1
\end{pmatrix}=
\begin{pmatrix}
0\\5
\end{pmatrix}$$
Published by Isshin Inada
Edited by 0 others
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