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
xz_007 [3.2K]
2 years ago
11

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of th

e corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.
Mathematics
1 answer:
Aliun [14]2 years ago
3 0

Answer:

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

A=\left[\begin{array}{ccc}-3&0&1\\2&-4&2\\-3&-2&1\end{array}\right]

to find the eigenvalues of the matrix you use the following:

det(A-\lambda I)=0

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

A-\lambda I=\left[\begin{array}{ccc}-3-\lambda&0&1\\2&-4-\lambda&2\\-3&-2&1-\lambda\end{array}\right]

and by taking the determinant:

[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-\lambda)+(2)(-2)(-3-\lambda)]=0\\\\-\lambda^3-6\lambda^2-12\lambda-16=0

and the roots of this polynomial is:

\lambda_1=-4\\\\\lambda_2=-1+i\sqrt{3}\\\\\lambda_3=-1-i\sqrt{3}

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

You might be interested in
Find the surface area of composite figures
Aleonysh [2.5K]

  • Answer:

<em>429 cm²</em>

  • Step-by-step explanation:

<em>A(blue) =</em>

<em>= 2×6cm×10cm + 2×6cm×8cm + 8cm×10cm + (8cm×10cm - 5cm×4cm)</em>

<em>= 120cm² + 96cm² + 80cm² + 60cm²</em>

<em>= 356 cm²</em>

<em>A(green) =</em>

<em>= 4cm×5cm + 2×5cm×5cm/2 + 4cm×7cm</em>

<em>= 20cm² + 25cm² + 28cm²</em>

<em>= 73 cm²</em>

<em>A(total) =</em>

<em>= A(blue) + A(green)</em>

<em>= 356 cm² + 73 cm²</em>

<em>= 429 cm²</em>

6 0
3 years ago
Read 2 more answers
What is the value of x in 2(5x) = 14?
Ray Of Light [21]

Answer:

x= 7/5

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
the scale on a map is 2 centimeters equals 15 Miles Dave measures the distance to the next town at 7 centimeters how many miles
jeka57 [31]
52.5 is the exact answer <span />
6 0
3 years ago
Whats the area below
Troyanec [42]

Step-by-step explanation:

3.5*9.0= 31.5cm²

2*2=4  4/2=2

2*2=4

5*2=10  10/2=5

5+4+2+31.5= 42.5cm²

8 0
2 years ago
If the sides of a triangle and area is given. How to find perimeter​
almond37 [142]

Answer:

add it up to see if it's 180

6 0
3 years ago
Read 2 more answers
Other questions:
  • Vertex Z of trapezoid WXYZ has coordinates (−9, 9).
    6·1 answer
  • Help plz! Use the slope formula to find the missing coordinate. m = 2, A(_, 0), B(5, 10)
    12·1 answer
  • Find the value of y.
    15·1 answer
  • Reduce the fraction 6x/12x to lowest terms.
    11·2 answers
  • A card is drawn from the numbered from 5 to 30 find the probability of getting square or even numbered card
    9·1 answer
  • If I have more 15 Pokemon cards than Austin, which expression shows how many |<br>have?​
    12·1 answer
  • The Cramer's Rule states that, in a system of equation in two unknowns, in which determinants D is not 0, X=_____and Y=_____.​
    11·1 answer
  • What is the slope of a line with the cords (-3,2) (-1,-1)
    13·1 answer
  • In Texas, the coldest temperature ever recorded is
    10·1 answer
  • The following functions give the populations of four towns with time tt in years.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!