Matrix Exponential and Differential Equations

Matrix Exponential and Differential Equations

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
HSN.VM.C.10

Standards-aligned

Created by

Emma Peterson

FREE Resource

Standards-aligned

CCSS.HSN.VM.C.10
The video tutorial explains how to compute the matrix exponential e^tA for a 2x2 matrix A with specific entries. It covers the process of finding eigenvalues and eigenvectors, addressing defective eigenvalues, and calculating the matrix exponential. The tutorial also demonstrates solving the differential equation x' = Ax with given initial conditions using the matrix exponential.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary task in the given problem?

To compute the matrix exponential and solve a differential equation.

To find the determinant of a matrix.

To calculate the inverse of a matrix.

To solve a system of linear equations.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the algebraic multiplicity of the eigenvalue found?

Four

Three

Two

One

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why can't the general procedure be used in this case?

Because the matrix is not square.

Because there are no eigenvalues.

Because the matrix is singular.

Because there is only one linearly independent eigenvector.

Tags

CCSS.HSN.VM.C.10

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is special about matrix B in this context?

B is a singular matrix.

B is a diagonal matrix.

B is an identity matrix.

B squared equals the zero matrix.

Tags

CCSS.HSN.VM.C.10

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the matrix exponential e^TB simplified in this scenario?

As a diagonal matrix.

As the zero matrix.

As B squared.

As I plus TB.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of e^(2tI) in the matrix exponential derivation?

A matrix with all entries equal to e^(2t).

An identity matrix.

A diagonal matrix with e^(2t) on the diagonal.

A zero matrix.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial condition given for solving the differential equation?

X(0) = [0, 0]

X(0) = [1, 2]

X(0) = [2, 1]

X(0) = [1, 1]

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