Understanding Linear Transformations and Transformation Matrices

Understanding Linear Transformations and Transformation Matrices

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSN-VM.B.5A, HSN.VM.A.1, HSN.VM.C.11

+2

Standards-aligned

Created by

Olivia Brooks

FREE Resource

Standards-aligned

CCSS.HSN-VM.B.5A
,
CCSS.HSN.VM.A.1
,
CCSS.HSN.VM.C.11
CCSS.HSN.VM.C.8
,
CCSS.HSN-VM.B.5B
,
The video tutorial explains linear transformations using standard basis vectors in R3. It details how vectors u, v, and w correspond to e1, e2, and e3, respectively. The transformation matrix is constructed by using the transformations of these basis vectors, where each transformation provides a column of the matrix. The tutorial concludes with a summary of how these transformations form the matrix.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a linear transformation in the context of vectors u, v, and w?

A way to find the inverse of a vector

A method to add vectors together

A mapping of vectors to another set of vectors

A process that scales vectors by a constant factor

Tags

CCSS.HSN.VM.A.1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is a standard basis vector in R3?

Vector (1, 1, 1)

Vector (0, 0, 0)

Vector (1, 0, 0)

Vector (2, 2, 2)

Tags

CCSS.HSN.VM.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is vector u represented in terms of standard basis vectors?

As vector e3

As vector e1

As vector e4

As vector e2

Tags

CCSS.HSN.VM.A.1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of transforming standard basis vectors?

It is used to calculate the inverse of a matrix

It helps in finding the determinant of a matrix

It determines the transformation matrix

It is used to solve linear equations

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which vector transformation gives the first column of the transformation matrix?

Transformation of vector e1

Transformation of vector e3

Transformation of vector e2

Transformation of vector e4

Tags

CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of transforming vector v, which is e2?

Vector (4, -4, 5)

Vector (5, -2, 5)

Vector (0, 2, 1)

Vector (1, 0, 0)

Tags

CCSS.HSN.VM.C.11

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which vector transformation results in the third column of the transformation matrix?

Transformation of vector e1

Transformation of vector e2

Transformation of vector e3

Transformation of vector e4

Tags

CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

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