Answer ASAP with explanation and will give brainlist

A = 4 0 0 1 3 0 −2 3 −1 Find the characteristic polynomial for the matrix A. (Write your answer in terms of λ.) Find the real ei

Illusion [34]

Answer:

Step-by-step explanation:

We are given the matrix

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

a) To find the characteristic polynomial we calculate $\text{det}(A-\lambda I)=0$ where I is the identity matrix of appropiate size. in this case the characteristic polynomial is

$\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0$

Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is

$(4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0$

which is the characteristic polynomial of A.

b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are $\lambda=4,3,-1$

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression $A-\lambda I$ and solve the system $(A-\lambda I)x =0$ by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider $\lambda = 4$ . We get the matrix

$\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right]$

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

$(x,y,z) = (5z,5z,z) = z(5,5,1)$

So, the base for this eigenspace is the vector (5,5,1).

If $\lambda = 3$ then the base is (0,4,3) and if $\lambda = -1$ then the base is (0,0,1)

3 0

3 years ago

Determine the quotient: 2 4 over 7 ÷ 1 3 over 6.

bulgar [2K]

Answer:

144/91

Step-by-step explanation:

24/7 ÷ 13/6

Keep the first fraction the same, change the sign, and flip the last fraction to solve

24/7 × 6/13 = 144/91

6 0

3 years ago

Read 2 more answers

When does a football hurled across a field have the lowest gravity force (A) when it has just left the quarterbacks hand. (B) wh

Svetllana [295]

Answer:

A

Step-by-step explanation:

I believe this because this is when it has the most amount of force pushing it, so I believe that A is the answer. Please correct me if I am wrong.

3 0

3 years ago

Find the Greatest Common Factor of the Numerator and Denominator

myrzilka [38]

Answer:

2

Step-by-step explanation:

i fink no very is not good becauese it nit nivr so i thimk

5 0

3 years ago

A sphere of diameter 10 inches is cut by a plane which passes through its center. Find the area of the cross-section, leaving th

sveticcg [70]

The area would be 25π inches.

Since the cross-section goes through the center of the sphere it will be a circle. The area of a circle is given by A = πr²; for our circle, since the diameter is 10 inches, the radius is 5;

A = π(5²) = 25π

5 0

4 years ago