Eigenvalues and Eigenvectors Concepts

Eigenvalues and Eigenvectors Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
6.EE.C.9, 8.EE.C.8B

Standards-aligned

Created by

Sophia Harris

FREE Resource

Standards-aligned

CCSS.6.EE.C.9
,
CCSS.8.EE.C.8B
The video tutorial explains how to find an eigenvector for a 3x3 matrix with an eigenvalue of 2. It begins by setting up the equation involving the matrix, eigenvalue, and identity matrix. The process involves subtracting matrices, solving the system using an augmented matrix, and parameterizing the solution. The tutorial concludes by selecting a specific eigenvector from the possible solutions, emphasizing that it cannot be the zero vector.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the eigenvalue given in the problem for the 3x3 matrix?

1

2

4

3

Tags

CCSS.6.EE.C.9

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What operation is performed on the identity matrix in the eigenvector equation setup?

Multiplication

Subtraction

Division

Addition

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the augmented matrix, which column lacks a pivot, indicating a free variable?

Column three

Column two

Column one

None

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of x3 in the reduced echelon form of the augmented matrix?

1

0

x2

x1

Tags

CCSS.8.EE.C.8B

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the free variable x2 parameterized in the solution?

x2 = -3t

x2 = 0

x2 = t

x2 = 1

Tags

CCSS.6.EE.C.9

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for x1 in terms of the parameter t?

x1 = 3t

x1 = 0

x1 = -3t

x1 = t

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What form do the eigenvectors take when parameterized by t?

(t, -3t, 0)

(0, 0, 0)

(-3t, t, 0)

(t, t, t)

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