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Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 5.3
Overview
Diagonal matrices are very simple. Theyre easy to multiply with other matrices and vectors, theyre
already in echelon form, and its very easy to determine
1.
Let
11 2
A: 2 2 -2
01
12
0 0 610
(a) Find a basis for the column space of A, and determine the rank of A.
1,. z 0 l izvlz \-l 7. 0\ 27 ~\ 20%
[Z L2 I 201% 8 3-0 | 0]ES7LO O v_(Q/\ O
O 0 (ail (0"0 IX
00 000
boys Qu Qdomn SPOLQQH"
RH E]
y )(g Vuo
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Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 6.3
Overview
Recall that Section 6.2 introduced the orthogonal projection of y onto u, which can be thought of
geometrically as the shadow cast by y on u. Alternately,
Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 6.1
Overview
A common technique in statistical analysis is the method of least squares. Although this method
can be applied in its simplest forms with no reference to m
Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 5.1
Overview
The equation P q = q used to find the steady-state vector q of a stochastic matrix P is a specific
case of the equation Ax = x. Solving Ax = x is sometimes
Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 6.2
Overview
Now that weve established a notion of perpendicularity in higher dimensions, we consider a preliminary application of this notion. An orthogonal basis, i.e
Adam Gutter
21-240 Matrix Algebra with Applications
Fall 2016
Guided Practice: Section 5.5
Overview
Up until this point, all eigenvalues and eigenvectors have been real-valued, which allows us to
interpret an eigenvalue A as a scaling factor and an eigenv