Matrix Exponential and Eigenvalues

Matrix Exponential and Eigenvalues

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
HSA.REI.C.9, HSN.VM.C.8

Standards-aligned

Created by

Emma Peterson

FREE Resource

Standards-aligned

CCSS.HSA.REI.C.9
,
CCSS.HSN.VM.C.8
The video tutorial explains how to compute the matrix exponential e^At for a 2x2 matrix A with specific entries. It covers determining eigenvalues and eigenvectors, and using them to find the matrix exponential. The tutorial also demonstrates finding the general solution to the differential equation X' = AX using the matrix exponential. The process involves setting up equations, simplifying, and performing matrix operations to achieve the final solution.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary goal of the problem discussed in the video?

To find the determinant of a matrix.

To determine the inverse of a matrix.

To solve a quadratic equation.

To compute the matrix exponential and find the general solution for X' = AX.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in determining the eigenvalues of a matrix?

Solving a system of linear equations.

Finding the inverse of the matrix.

Setting up the equation det(A - λI) = 0.

Calculating the trace of the matrix.

Tags

CCSS.HSA.REI.C.9

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many linearly independent eigenvectors are needed to proceed with the general procedure?

Four

Three

Two

One

Tags

CCSS.HSA.REI.C.9

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the form of matrix A in the diagonalization process?

A = D * E * E^(-1)

A = E * D * E^(-1)

A = E^(-1) * D * E

A = E * E^(-1) * D

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main diagonal of matrix D composed of in the diagonalization process?

Ones

Random numbers

Zeros

Eigenvalues

Tags

CCSS.HSN.VM.C.8

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of multiplying the matrices in the computation of e^(tA)?

An identity matrix

A zero matrix

A 2x2 matrix with specific exponential terms

A scalar value

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final form of the matrix exponential e^(tA)?

A scalar

A vector

A matrix

A polynomial

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