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scoundrel [369]
3 years ago
11

Consider the matrices -2 -1 1 4 1 A = B = 4 -2 4 -2 -2 4 -2 1 -1 (a) Verify that they are diagonalizable and that they commute.

(b) Find the eigenvalues and eigenvectors of A and verify that its spectrum is nondegenerate. (c) Show that the eigenvectors of A are eigenvectors of B as well.

Mathematics
1 answer:
Phoenix [80]3 years ago
6 0

Answer:

Explanation to answers are shown in the attachment

Step-by-step explanation:

This is a long solution but the detailed step by step and appropriate mathematical manipulation has been done as shown in the attachment.

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HELPPPPPPPP!!!!!!!!!!
Novosadov [1.4K]

Step-by-step explanation:

98 = 188t - 16t^2

-16t^2 + 188t = 98

-16t^2 + 188t - 98 = 0

8t^2 - 94t + 49 = 0

Use the quadratic formula with a = 8 , b = -94 , c = 49 to get the solutions

t = [(47 - root 1817) / 8]≈ 0.55

and

t = [(47 + root 1817) / 8] ≈ 11.20

8 0
3 years ago
A 29- m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 33 . Find the length
prohojiy [21]

Answer:

About 17.7 meters.

Step-by-step explanation:

This can be solved by imagining the triangle formed by the building and its shadow. The hypotenuse of the triangle, the distance from the tip of the building to the tip of the shadow, is 34 meters, and one of the legs is 29 meters. Therefore, we can use the Pythagorean theorem to find that the third side is . Hope this helps!

6 0
3 years ago
A rectangular flower bed is five feet longer than it is wide. its area is eighty-four square feet.
777dan777 [17]
Lets say w is the width of the flower bed. We can make an equation to find the area.
The length of the of the flower bed is (w+5) and the width is w.
To find the area we need to multiply the length(w+5) by the width(w) and set it equal to 84,
(w+5)(w)=84
w^2 +5w=84
Using the quadratic equation you get the solutions of 7 and -12. Since 7 is positive it is our width. Our length is 7+5 or 12.
3 0
3 years ago
3/4 - 2/7 = ? pls help me because I can get grounded
Leona [35]

Answer:

1/7

Step-by-step explanation:

&&5_4_&&&&&&&&&&&&&---

7 0
3 years ago
A square of side length s lies in a plane perpendicular to a line L. One vertex of the square lies on L. As this square moves a
user100 [1]

Answer:

Part (A) The required volume of the column is s^2h.

Part (B) The volume be s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}.

Step-by-step explanation:

Consider the provided information.

It is given that the we have a square with side length "s" lies in a plane perpendicular to a line L.

Also One vertex of the square lies on L.

Part (A)

Suppose there is a square piece of a paper which is attached with a wire through one corner. As you blow it up it spins around on the wire.

This square moves a distance h along​ L, and generate a​ corkscrew-like column with square​.

The cross section will remain the same.

So the cross section area of original column and the cross section area of twisted column at each point will be the same.

The volume of the column is the area of square times the height.

This can be written as:

s^2h

Hence, the required volume of the column is s^2h.

Part (B) What will the volume be if the square turns twice instead of once?

If the square turns twice instead of once then the volume will remains the same but divide the volume into two equal part.

s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}

Hence, the volume be s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}.

5 0
3 years ago
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