Unit 3

Question 1

What is a matrix trace?

Answer 1

The sum of the leading diagonal terms

Question 2

What does symmetric mean?

Answer 2

Atranspose=A

Question 3

What does Skew-Symmetric mean?

Answer 3

Atranspose=-A

Question 4

What is the transpose of a matrix?

Answer 4

A matrix where the rows and columns have been swapped

Question 5

What is Guassian elimination?

Answer 5

Converting the matrix to an upper triangular to solve one term, which can then be used to solve the above equations

Question 6

What is Row-Echelon form?

Answer 6

Form once converted to Upper Triangular

Question 7

What is Reduced Row-Echelon form?

Answer 7

Form once converted to Unit Matrix

Question 8

What is the rank of a matrix?

Answer 8

The # of non-zero in the Upper Triangular form?

Question 9

What is an Eigenvector?

Answer 9

A non-zero vector that, when multiplied by the subject matrix, produces a scalar product of itself

Question 10

What is an Eigenvalue?

Answer 10

The scalar k where AX=kX

Question 11

When do the Eigenvalues have non-trivial solutions?

Answer 11

When |A-kI|=0 where I is the unit vector equal in size to A

Question 12

What is the sum from 1 to n of integers?

Answer 12

Sn=n/2(n+1)

Question 13

What is the sum from 1 to n of x^2?

Answer 13

Sn=n/6(n+1)(2n+1)

Question 14

For a sequence F=a+(n-1)d, what is the sum to n?

Answer 14

Sn=n/2(2a+(n-1)d)

Question 15

What is the sum to in of a geometric series ar^x

Answer 15

Sn=a((1-r^n)/(1-r))

Question 16

If S\infty of Ck is convergent and Uk is less than or equal to Ck

Answer 16

Uk is also convergent

Question 17

What is d’Alembert’s Ratio Test?

Answer 17

Find the limit of U(n+1)/Un for series Uk
If this limit >1 - Divergent
<1 - Convergent

Question 18

What is the radius of convergence, r, of a power series?

Answer 18

|a(n)/a(n+1)|

Question 19

When is a power series absolutely convergent?

Answer 19

When |x| is less than r