Math 220 (Fall 2013): Lecture Notes and Videos on Introductory Linear Algebra
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Copyright: I (Bala Krishnamoorthy) hold the copyright
for all lecture scribes/notes, documents, and other
materials including videos posted on these course web
pages. These materials might not be used for commercial
purposes without my consent.
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Scribes from
all lectures so far (as a single big file)
| Lec | Date | Topic(s) | Scribe | Video |
| 1 | Aug 20 | syllabus, intro
to mymathlab.com, 2D example
(2 linear equations in 2 variables), graphical solution
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Scb1 |
Vid1 |
| 2 | Aug 22 | Gaussian
elimination, augmented matrix, elementary row operations (EROs), \(
\begin{bmatrix} 0 & 0 & \cdots & 0 & | & {\bf \star}\neq 0 \end{bmatrix}\) --
inconsistent system
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Scb2 |
Vid2 |
| 3 | Aug 27 | nonzero row,
leading entry, echelon form and reduced echelon form, row reduction
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Scb3 |
Vid3 |
| 4 | Aug 29 | symbolic notation
for echelon form, basic and free variables, parametric form of
solutions, vectors, linear combination, span,
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Scb4 |
Vid4 |
| 5 | Sep 3 | pictures of
span in 2D & 3D, span all of \( \mathbb{R}^n \), matrix form \( A
\mathbf{x} = \mathbf{b} \)
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Scb5 |
Vid5 |
| 6 | Sep 5 |
\( A \mathbf{x} = \mathbf{b} \) consistent \( \forall \mathbf{b}\) iff \(A\) has a pivot in every row, homogenous system, trivial solution, parametric vector form of solutions
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Scb6 |
Vid6 |
| 7 | Sep 10 | Solutions to
\(A\mathbf{x} = \mathbf{b}\) in relation to those of \(A\mathbf{x} =
\mathbf{0}\), linear independence (LI) of vectors, special case of LI
for a single vector
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Scb7 |
Vid7 |
| 8 | Sep 12 | LI of two vectors,
with \( \mathbf{0} \), \(\{\mathbf{v}_1,\dots,\mathbf{v}_n\}\) is LD
when \( \mathbf{v}_i \in \mathbb{R}^m\) and \(n > m\),
(matrix) transformations, (co)domain, image, range
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Scb8 |
Vid8 |
| 9 | Sep 17 |
review of problems from Sections 1.4, 1.5, and 1.7 (as we are slowing down:-)
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Scb9 |
Vid9 |
| 10 | Sep 19 |
linear transformations (LT), preserve vector addition and scalar
multiplication, matrix of an LT
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Scb10 |
Vid10 |
| 11 | Sep 24 |
matrix of an LT, geometric transformations - rotation, reflection,
shear, projection, onto and one-to-one transformations
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Scb11 |
oops:-( |
| 12 | Sep 26 |
problems on matrix of LT, onto and one-to-one LTs, onto iff pivot in
every row, 1-to-1 iff pivot in every column
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Scb12 |
Vid12 |
| 13 | Oct 1 |
review of practice midterm exam
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Scb13 |
Vid13 |
| 14 | Oct 3 |
midterm
| exam | |
| 15 | Oct 8 |
class canceled
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| 16 | Oct 10 |
By Prof. McDonald:
matrix multiplication, power and transpose of a
matrix; notes from
Prof. McDonald
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Scb16 |
NA |
| 17 | Oct 15 |
inverse of a matrix, inverse of \(2 \times 2 \) matrix,
determinant, properties of matrix inverses |
Scb17 |
Vid17 |
| 18 | Oct 17 |
inverting \( n \times n \) matrix, \( [ A | I] \longrightarrow [ I
| A^{-1} ]\), using properties of inverses, invertible matrix theorem
(IMT) |
Scb18 |
Vid18 |
| 19 | Oct 22 |
invertible matrix theorem (IMT) - statements
(a)-(l), problems using IMT |
Scb19 |
Vid19 |
| 20 | Oct 24 |
subspaces - of \( \mathbb{R}^2 \), generated by \(\{
\mathbf{v_1},\dots,\mathbf{v_p}\}\); column and null spaces of \(A\) -
\( \operatorname{Col} A, \operatorname{Nul} A\), basis for a
subspace |
Scb20 |
Vid20 |
| 21 | Oct 29 |
By Prof. McDonald:
bases for \( \operatorname{Col} A\),\(
\operatorname{Nul} A\), dimension of a subspace, rank,
rank theorem, IMT (contd..);
Prof. McDonald's notes
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Scb21 |
NA |
| 22 | Oct 31 |
class canceled
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| 23 | Nov 5 |
coordinates of \({\bf x}\) in a basis \(\mathcal{B}\): \( [{\bf
x}]_{\mathcal{B}} \), more on dimension and rank, determinant of a \(
3 \times 3\) matrix, expand along Row 1 |
Scb23 |
Vid23 |
| 24 | Nov 7 |
Computer project, intro to
MATLAB, \(n \times n\) determinant by expanding along Row 1, cofactor
expansion along any row/column |
Scb24 |
Vid24 |
| 25 | Nov 12 |
\(\operatorname{det}\) of triangular matrix,
\(\operatorname{det}(A)\) using EROs, \(A^{-1}\) exists
\(\Leftrightarrow \operatorname{det}(A) \neq 0\),
\(\operatorname{det}(A^T) = \operatorname{det}(A)\),
\(\operatorname{det}(AB) =
\operatorname{det}(A)\operatorname{det}(B)\) |
Scb25 |
Vid25 |
| 26 | Nov 14 |
\(\operatorname{det}(B^{-1}AB) = \operatorname{det}(A)\) when
\(\operatorname{det}(B) \neq 0\), eigenvalues and eignevectors, \((A^T
= A) \Rightarrow \) all eignvalues of \(A\) are real
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Scb26 |
oops:-( |
| 27 | Nov 19 |
testing eigenvalues/eigenvectors, eigenspace, eigenvalues of
triangular matrices are diagonal entries, all rows of \(A\) adding to \(s\)
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Scb27 |
Vid27 |
| 28 | Nov 21 |
characteristic polynomial & equation, multiplicity of eigenvalue,
similar matrices, EROs and
eigenvalues, Matlab for
project
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Scb28 |
Vid28 |
| 29 | Dec 3 |
scalar (or dot) product of vectors, length of vector, orthogonal
vectors and sets, orthogonal basis, orthogonal projection
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Scb29 |
Vid29 |
| 30 | Dec 5 |
write vector \(\mathbf{y}\) as \(\mathbf{y_u} + \mathbf{v}\),
where \(\mathbf{y_u} \in\) span\(\{\mathbf{u}\}\) and \(\mathbf{v}
\perp \mathbf{y_u}\), review
for final exam
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Scb30 |
Vid30 |
Last modified: Fri Dec 06 08:27:24 PST 2013
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