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I am Lyosha [343]
3 years ago
13

Explain why a 2x2 matrix can have at most two distinct eigenvalues

Mathematics
1 answer:
VladimirAG [237]3 years ago
5 0
Hey there. Hope I can help.

So lets say that a 2 * 2 matrix (A) has three distinct eigenvalues.

You need to remember that the eigen vectors state V_1,...,v_r which correspond to the distinct Eigen values λ_1,...,λ_n of an n * n matrix, then our set {V_1,...,v_r} is linearly independent. 

Which we can now tell by this theorem that three linearly independent eigenvectors correspond which is literally absurd.

The reason for this is because the matrix A is only two dimensional which means the three vectors belong to R^2. So any set {V_1,...,v_r} in R^n would be linearly independent if r > n since (r = 3) > (n = 2). These three eigenvectors then become linearly independent. Therefore the 2 * 2 matrix can only have 2 atmost.
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For his birthday, Tyrone's parents gave him $7,790.00 which they put into a savings account that earns 15% interest compounded m
torisob [31]

Answer:

5 years and 5 months

Step-by-step explanation:

<u />

<u>Compound Interest Formula</u>

\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • n = number of times interest applied per time period
  • t = number of time periods elapsed

Given:

  • A = $17,474.00
  • P = $7,790.00
  • r = 15% = 0.15
  • n = 12
  • t = number of years

Substitute the given values into the formula and solve for t:

\implies \sf 17474=7790\left(1+\dfrac{0.15}{12}\right)^{12t}

\implies \sf \dfrac{17474}{7790}=\left(1.0125}\right)^{12t}

\implies \sf \ln\left(\dfrac{17474}{7790}\right)=\ln \left(1.0125}\right)^{12t}

\implies \sf \ln\left(\dfrac{17474}{7790}\right)=12t \ln \left(1.0125}\right)

\implies \sf t=\dfrac{\ln\left(\frac{17474}{7790}\right)}{12 \ln \left(1.0125}\right)}

\implies \sf t=5.419413037...\:years

Therefore, the money was in the account for 5 years and 5 months (to the nearest month).

3 0
1 year ago
Read 2 more answers
What’s the answer (anyone ?)
alexgriva [62]

Answer: Idek if that's a question

Step-by-step explanation:

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posledela

Answer:

3003 units^3.

Step-by-step explanation:

Just multiply the dimensions :

11 * 13 * 21

= 143 * 21

= 3003 units^3.

8 0
3 years ago
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