Question : I need to solve Matrix problems (Augment them or reduce them...)
I know how to enter the matrix into the calculator like 3X3 for [A] etc...
What do I need to do to solve them??
I know I go to second matrix then I go over to Math...
What do I hit next???
And how do I put it in??? If I put it in as say....
augment([A]) it comes up with an error screen saying ERR Argument....
I am very frustrated and very confused...
I don't know how to even approach these problems and my teacher doesn't h..
Answer : so let A be a 3 x 4 matrix...you enter all the entries..4th entry in each row is the constant on the right of the = sign....then go to math ops and choose ' rref' A...answers will be in the 4th column.....3,-2,0
Question : So that I can perform Gauss-Jordan elimination.
The values are the following:
Answer : Hit [2ND] + [MATRIX] (push the [X^-1])
Scroll to the right to EDIT
Input the order of the matrix (in this case 3 x 4):
Input each value into the matrix, pressing enter as you go:
So you will hit 3 > enter > 4 > enter > 3 > enter > 1 > enter > etc.
Once you have your matrix values, push [2ND] and [Quit]
Hit [2nd] and [Matrix]
Scroll to the right to Math
Scroll down to rref( and push enter
Then hit [2nd] and [matrix] again.. select your matrix and push enter
Push enter again on the screen and you should find your solution.
Question : I know how to derive the inverse matrix using reduced-row-echelon form(just by augmenting the matrix with its identity), but I never learned how to use determinants to do the same task. thank you for your help ahead of time.
Answer : If A is invertible, then A can be expressed in terms of the adjugate matrix of A, as
A = (1/det(A))adj(A),
where adj(A) can itself be calculated in terms of determinants of submatrices of A as follows:
(1) Define the minor M_[ij] of A to be the (n-1)-by-(n-1) matrix that results from deleting row i and column j from A.
(2) Define the cofactor matrix C of A as
C_[ij] = (-1)^(i+j)det(M_[ij]).
(3) Finally, define adj(A) = C^ .
Using Laplace's formula for expanding the determinant of a matrix, one can show
A adj(A) = det(A)I,
so if A is invertible,
A = (1/det(A))adj(A).