UC Davis Linear Algebra Worksheet

UC Davis Linear Algebra Worksheet

UC Davis Linear Algebra Worksheet

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QUIZ # 2
* Turn this quiz by 3/13
Show all the steps
1) (8) Find the determinant of A by reducing the matrix to a reduced row echelon form,
using EROs ( elementary row operation)

=
2 2 2
3 4 5
2 2 4
A
2) (8) If |A|= 4 and A, B are
3 3
matrices,
( ) 
8
3
det 3
2 3
=
− B A
. What is |B|?
3) (8) Find the distance of the point (3,4) to the line
2y − x = 5
4) (10) Follow the result of above question, find the distance of the point
(3,−2,1)
to the line
2x − y + 3z = 2
Note: You only use the cross product for this question
5) (6) Given
= 6
g h i
d e f
a b c
. Find
g d h e i f
d e f
a b c
2 2 2
/ 2 / 2 / 2
5 5 5
− − −

Math 410, Linear Algebra      Chapter 1.7                                                     Fall 2020

Chapter 1.7 Diagonal, Triangular and Symmetric Matrices

Example 1: The product of a matrix A and with its transpose is symmetric

Example 2:

Example 3:      Determine whether  the matrix is symmetric

1. a) . Since  not symmetric
2. b)     Since  they are symmetric