If a 2x2 matrix has the same two eigenvalues as another 2x2 matrix, what conclusions can you infer about the two matrices? make some hypotheses and attempt to prove them, or refute them via counterexamples.

Answer with explanation

It is given that , two matrix, having order , 2×2, has same eigenvalue.Let P, and Q be two matrix.

Suppose,

→→P-αI

   Where, α is a scalar, and I is Identity matrix having order , 2×2.

When we evaluate the determinant , it will be in the form of Quadratic function ,which we call Characteristic Polynomial , which will give two eigen values.

→→Now, it is given that, two matrix having same order, has same eigen values , means characteristic polynomial of two equation will be same.

→→If you solve the Characteristic equation that is

| P -αI |=0

You will get two Eigenvalues.

→The two matrrix will be identical, that is same if they have same eigenvalue.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

$9.89

step-by-step explanation:

9.90 = p x .06 x .25 (3/12 changed to a decimal)

9.90 = p x 0.015

9.90 - 0.015 = p

9.89 = p