Proving Matrix Equality: A^3+4A^2-2A+7i=0 Implies A^T Also Satisfies It?

  • Thread starter ahmed dawod
  • Start date
In summary, proving something involves providing evidence or logical reasoning to support a claim or statement. Anyone can theoretically prove something, but it may require specialized knowledge and resources. The steps to proving something involve identifying a hypothesis, designing an experiment, analyzing results, and drawing a conclusion. Different fields may have different types of proof such as empirical evidence in science and logical reasoning in mathematics. However, proof is not always conclusive as there may be limitations or new evidence that can change previous understandings.
  • #1
ahmed dawod
3
0
1. show that if a square matrix A satisfies A^3+4A^2 -2A+7i=0 then so does A^T

i is the identity matrix






The Attempt at a Solution



I tried to multiply the equation by A^T but all in vain
 
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  • #2
Use:
[tex](A+B)^T = A^T + B^T \qquad (AB)^T = A^TB^T \qquad (cA)^T = cA^T[/tex]
to compute the transpose by using:
[tex]0 = 0^T = (A^3 + 4A^2 - 2A + 7I)^T[/tex]
 
  • #3
thanks
this is useful

problem solved:biggrin:
 

1. How do you prove something?

Proving something involves providing evidence or logical reasoning to support a claim or statement. This can include conducting experiments, gathering data, or using mathematical equations.

2. Can anyone prove something?

In theory, anyone can prove something as long as they have the necessary knowledge, skills, and resources to do so. However, not all claims can be definitively proven and some may require specialized expertise.

3. What are the steps to proving something?

The steps to proving something can vary depending on the subject matter, but generally involve identifying a hypothesis or claim, designing an experiment or data collection method, analyzing the results, and drawing a conclusion based on the evidence.

4. Are there different types of proof?

Yes, there are different types of proof depending on the field of study. In science, proof is often based on empirical evidence and experimentation. In mathematics, proof is based on logical reasoning and deductive arguments.

5. Is proof always conclusive?

Proof is not always conclusive. In some cases, there may be limitations to the evidence or alternative explanations that cannot be completely ruled out. Additionally, new evidence or advancements in knowledge may lead to a different understanding of a previously proven concept.

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