Math Help

Archive for the ‘Matrices’ Category

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!

Find the value of K

K[ 3 , -1 ] = [ -3/4 , 1/4 ]
–[ 5 , -4 ]—-[ -5/4 , 1 ]

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

Matrix transpose is a math method where the rows and columns of a matrix interchange. The definition of a matrix transpose is show below.

Definition of transpose

The definition of transpose is to move a term from one side of an equation to the other side of the equation with a corresponding change of sign. For example, if we were to transpose the equation:

x – y = 2

we will get the transposed equation of x = y +2

Definition of matrix transpose

and the matrix transpose of this matrix is: