I need help writing an creating an invertible matrix!!!!?

Question

how do I write an invertible matrix that has no 1, -1, or 0 in it? is there a way or formula in doing that?

please don't give me examples from any math textbook, thank you!!!!

Answer 1

How about a 1 X 1 matrix with an element that is not -1, 1 or 0.



It will be invertible, and satisfy your requirements.



Additionally, if you want something that doesn't seem too 'cheap', use the observation that any invertible matrix has a non-zero determinant.



So, use a 2 X 2 matrix with the elements a, b, c, and d.

Let ab - cd = 0

Choose values for a, b, and c that are not -1, 1, or 0.

Solve for d, and voila, you get a matrix that satisfies your requirements.

Answer 2

Every non-zero 1x1 matrix is invertible. So, just give the matrix [10]. Its inverse is [1/10].



A 2x2 matrix



a b

c d



is invertible if and only if the "cross products" ad and bc are not equal. So, just stick random numbers in for a, b, c, and d, and compare their cross products. If they're equal, you're screwed (and amazingly unlucky). Just change one number, and it will be inverible. For example:

2 4

3 6



That doesn't invert, because 2 * 6 = 3 * 4. But if I change one number:

2 40

3 6



Now it's inverible.

Answer 3

a matrix will be invertible if it's determinant is non-zero. So, consider a 2 x 2 matrix with entries,

a b

c d



the determinant is ad - bc. So, as long as you make a, b, c, and d such that the determinant is not zero, you're good.

Answer 4

in trouble-free terms to interchange what "Prince of ROCK!" reported. Matlab have moved a techniques flung from Maple. you would be able to do symbolic maths in Matlab despite if it would not would desire to be Maple. the main element grew to become despite if, Matlab in in fact a numerical gadget. it won't have the ability to help that plenty with the reading theory & fixing equations, till finally you choose for a numerical answer. it is needless to say super if it is the section you're in. Matlab isn't much less intense priced. It has opposition: Noteably octave, loose under linux. From memory octave would not have as sturdy photographs help.

Answer 5

the idea is to make it so that no column can be represented as a linear combination of other columns

[ 7 , 2 , 3

3, -2, 5

2, 7, 0 ]