Question

Prove or disprove: Can a symmetric matrix be necessarily diagonalizable?

Please show clear steps. Thank you.

Answer #1

can you please show all the steps thank you...
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n×n-matrix M is symmetric if M = M^t. Matrix M is
anti-symmetric if M^t = -M.
1. Show that the diagonal of an anti-symmetric matrix are
zero
2. suppose that A,B are symmetric n × n-matrices. Prove that AB
is symmetric if AB = BA.
3. Let A be any n×n-matrix. Prove that A+A^t is symmetric and A
- A^t antisymmetric.
4. Prove that every n × n-matrix can be written as the sum of a
symmetric and anti-symmetric matrix.

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a statement you have to show that the statement is false.
Equivalently, you can prove that the negation of the statement is
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(b) For...

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Please answer questions in clear hand-writing and show me the
full process, thank you so much (Sometimes I get the answer which
was difficult to read).

Matrix A is given as A =
0 2 −1
−1 3 −1
−2 4 −1
a) Find all eigenvalues of A.
b) Find a basis for each eigenspace of A.
c) Determine whether A is diagonalizable. If it is, ﬁnd an
invertible matrix P and a diagonal matrix D such that D =
P^−1AP.
Please show all work and steps clearly please so I can follow
your logic and learn to solve similar ones myself. I...

When we say Prove or disprove the
following statements, “Prove” means you show the
statement is true proving the correct statement using at most 3
lines or referring to a textbook theorem.
“Disprove” means you show a statement is wrong by
giving a counterexample why that is not true).
Are the following statements true or not? Prove or disprove
these one by one. Show how the random variable X looks in each
case.
(a) E[X] < 0 for some random...

Please show all steps thank you.
Determine the smallest n such that there exists nonisomorphic
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answer.

Please show all steps and work no how you got answer thank
you!
Please no script! Some people have bad script hand writing
please write normal ;[
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Find the present value of $3000 due at the end of 11years at 10%
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Use any method to solve the system of nonlinear equations.
Please show steps. Thank you.
x2 + y2 = 1
y = 20x2 - 1

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