## Why choose us?

We understand the dilemma that you are currently in of whether or not to place your trust on us. Allow us to show you how we can offer you the best and cheap essay writing service and essay review service.

# Linear Algebra Questions

Linear Algebra Questions

LINEAR ALGEBRA 2
Question 14
A 1 S>0, 5×7-6 2 = -1,
So, not positive definite
A 2 -1<0, so not positive definite.
A3 1>1, 1×100-10×10 = 0,
So, not positive definite
A 4 1>, 1×101-10×10 = 1
So, it is positive definite

If x 1 = 1, x 2 =-1, then this product is 0.

Question 18
Solutions:
K=A T A is symmetric positive definite if and only if A has independent columns
For, columns of A are independent. So A T A will be positive definite.
For, columns of A are independent. So A T A will be positive definite.
For, columns of A are independent. So A T A will not be positive definite.
Question 7
Since a matrix is positive-definite if and only if all its eigenvalues are positive, and since the
eigenvalues of A −1 are simply the inverses of the, eigenvalues of A, A −1 is also positive definite
(the inverse of a positive number is positive).

LINEAR ALGEBRA 3

Question 14
a. Positive
b. Negative definite
c. Indefinite
d. Negative definite

Question 15
a. False
b. False
c. True
d. True

LINEAR ALGEBRA 4
Question 32

Question 41
On the one hand, Ax =λMx is the same as C T ACy =λy (writing M = R T R for C = R −1 , and putting
Rx = y). Then y T By/y T y has its minimum value at λ 1 (B=CTAC), the least eigenvalue for the
generalized eigenvector problem. On the other hand, this quotient is equal to x T Ax/x T Mx, which
sometimes equals a 11/m11, e.g., when x equals the standard unit vector e1.

Problem Set 6.3
Question 2

LINEAR ALGEBRA 5

Question 5

As ��=0 corresponds with , does not enter the picture

LINEAR ALGEBRA 6

References

Bretscher, O. (2004). Linear Algebra with Applications, (3 rd ed.). New York, NY: Prentice Hall.
Farin, G., & Hansford, D. (2004). Practical Linear Algebra: A Geometry Toolbox. London: AK
Peters.
Friedberg, S. H., Insel, A. J., & Spence, L. E. (2002). Linear Algebra, (4 th ed.). New York, NY:
Prentice Hall.
Leon, S. J. (2006). Linear Algebra with Applications, (7 th ed.). New York, NY: Pearson Prentice
Hall.
McMahon, D. (2005). Linear Algebra Demystified. New York, NY: McGraw–Hill Professional.
Zhang, F. (2009). Linear Algebra: Challenging Problems for Students. Baltimore, MA: The
Johns Hopkins University Press.