Let
Solve the following matrix equation 
Archive for the ‘Linear Algebra’ Category
A possible HKAL Pure problem?
三月 5, 2009Let
(a) By expanding the determinant along the last row (or otherwise), show that det(A) is a cubic polynomial in 
(b) Show that 
(c) Using the relationship between the roots and coefficients of a polynomial (or otherwise), show that 
Preparing for the Exam (2)
二月 28, 2009Here are a collection of relatively easy problems:
1) Can you find a 4 by 4 matrix, that is NOT upper-triangular with charpoly being
2) When you have a matrix, always ask yourself the following questions: Read the rest of this entry ?
Answer to Basic Linear Algebra Questions (1)
二月 26, 2009The following is a list of basic questions you should know how to answer (by heart)
(1) Suppose 
Ans: 
(2) If 
Ans: Ax = 0. Read the rest of this entry ?
Hints to Selected Problems in HW 5
二月 17, 2009For 3. Answer the following mini questions:
(a) Let A = B + I, what is rank(A)?
(b) What is
(c) If 
Preparing for the Linear Algebra Final (1)
二月 17, 2009The following is a list of basic questions you should know how to answer (by heart)
(1) Suppose
(2) If 
Magic Squares (Proof)
二月 11, 2009In this post, we will prove two things:
Let 
1) That if 
2) I will find the dimension, as well as a basis for
For 1, Let 
Hints to Selected Problems in HW 4
二月 11, 20091b: Use part (a), Proposition 4.41 and rank-nullity.
2c: Use 2b, and HW problem 3a.
2e: what are the polynomials such that f’ = 0 ?
2f: Use rank-nullity.
2g: What is
2l: First find
The problems are available at:
Click here
Questions concerning Magic Squares and Matrices
二月 9, 2009A magic square is such that all row sums, column sums, and diagonal sums are equal, and we call this common sum the “magic number” for the magic square. Let’s look at the following well-known 3 by 3 magic square with magic number 15:
If we view this as a 3 by 3 matrix, what kind of properties does 
Here is what I found out: Read the rest of this entry ?
