Math Help

Posts Tagged ‘matrix’

Question: Math Matrices (matrix) Problem?

i have this question and ive been stuck on it for ever i just don’t understand it can someone help me out!

Answer: Bring the K inside the matrix and then pick any element to solve
[ 3K -K ] =
[ 5K -4K ]

[ -3/4 1/4]
[ -5/4 1 ]

3K=-3/4
K=-1/4

Algebra – Matrices – Gauss Jordan Method Part 1 Augmented Matrix

Question: any math majors? Matrices help?

so i understand how to add, subtract, and multiply Matrices ex: AB, A+B, A-B but I really don’t understand how to get the inverse. a step-by-step would really help out

Answer: for a 2×2 matrix
a b
c d
you just divide the matrix
d -b
-c a
by the determinant (ad-bc).

For a 3×3 matrix
a b c
d e f
g h i
calculate the matrix
a* b* c*
d* e* f*
g* h* i*
where these nine numbers are
(ei-fh) (ch-bi) (bf-ce)
(fg-di) (ai-cg) (cd-af)
(dh-eg) (bg-ah) (ae-bd)
[notice the pattern - each of these matrix elements is the determinant of a 2x2 matrix got by crossing out a row and a column in the original matrix]. This new matrix is called the ‘adjoint’ matrix.
Now divide the ‘adjoint’ matrix throughout by the determinant of the original matrix, which is
(aa* + bb* + cc*),
and you’ve got the inverse of
a b c
d e f
g h i

It’s tricky (you have to be very careful with the minus signs!).

The method generalizes for nxn Matrices. I hope you don’t want me to go into that (-:

Math Lessons : Solving a Matrix

What is an identity matrix?

An identity matrix is also called a unit matrix. An identity matrix is a square matrix in which:

• all the elements of the diagonal between the top left corner and the bottom right hand corner are ones and
• all the other elements are zeros.

Identify Matrices

Below are example of identity Matrices.

,

Property of the identity matrix

The identity matrix is very useful because of the following property which you can assume for all identity Matrices. If I represents the identity matrix and A is any other matrix, then:

Example of calculation with the identity or unit matrix