1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.
You might be interested in
Can you please help me??
Dominik [7]

Answer: B

Step-by-step explanation: I know

8 0
2 years ago
Simplify the following expression.<br> -21 - (-11)
Bumek [7]

Answer:

-10

Step-by-step explanation:

well you know that

(-)(-)=(+)

so we have

-21-(-11)\\\\=-21+11\\\\=-10

6 0
3 years ago
How do I find the slope if the fraction is improper? Do I leave it the same or?
Darina [25.2K]

Answer:

Leave it the same, it still works for the equation.

<em><u>Hope this helped! Have a nice day! Plz mark as brainliest!!! :D</u></em>

<em><u>-XxDeathshotxX</u></em>

4 0
3 years ago
Read 2 more answers
Find the x intercepts if the equation is 8x=-x^2+20
serious [3.7K]
Times both sides by -1
-8x=x²-20
add 8x both sides
0=x²+8x-20
factor
what 2 numbers multiply to get -20 and add to get 8
-2 and 10
0=(x-2)(x+10)
set to zero

x-2=0
x=2

x+10=0
x=-10


x intercepts at x=-10 and 2 or at the points
(-10,0) and (2,0)
7 0
3 years ago
PLEASE HURRY :,)
mart [117]

Answer:

A. The first quadrant of a coordinate grid is drawn. The title is Cake Stand. The horizontal axis label is Number of Cupcakes, and the scale is from 0 to 8 in increments of 1. The vertical axis label is Cost in dollars, and the scale is from 0 to 32 in increments of 4. Points are plotted at the ordered pairs 1,8 and 2,12 and 3,16.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the exact values of the six trigonometric functions of the angle(theta)
    14·1 answer
  • Which place is the 7 in?
    14·2 answers
  • twenty-five percent of the cowboys who participated in the Texas cattle drives were African Americans. True False
    6·1 answer
  • 3. Find the annual salary when the monthly salary is $4,725,
    6·2 answers
  • Jamie has 62 stickers Henry has 88 stickers. How many stickers must
    15·1 answer
  • Refer to the Lincolnville School District bus data. Information provided by manufacturers of school buses suggests the mean main
    8·1 answer
  • Solve the equation.<br> +8+3x=X-6<br> Ox=-18<br> Ox=-14<br> Ox=2<br> Ox=4
    11·1 answer
  • Please help me with ALL WORK SHOWN!! I will give you 15 points
    11·1 answer
  • A type of medicine is given in a 100-milligram dosage. The medicine comes in 14-gram bottles. How many 100-milligram dosages are
    15·1 answer
  • Y=-3+1/2x
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!