This video tutorial introduces matrix transformations, explaining how functions map from Rn to Rm using matrices. It covers key vocabulary such as domain, codomain, image, pre-image, and range. The tutorial provides examples of transformations from R3 to R2 and R2 to R3, demonstrating the process graphically. It concludes with a discussion on linear transformations, highlighting their properties and proving them using matrix operations.

What is a matrix transformation?

• A function that maps numbers to matrices

• A function that maps matrices to vectors

• A function that maps vectors to matrices

• A function that maps vectors from R^n to R^m using a matrix

What is the domain of a transformation T from R^n to R^m?

• R^n

• R^m

• The column space of the matrix

• The row space of the matrix

In a matrix transformation, what is the image of a vector?

• The domain of the transformation

• The input vector

• The output vector

• The matrix used for transformation

What is the range of a transformation T?

• The row space of the matrix

• The column space of the matrix

• The set of all output vectors

• The set of all input vectors

Tags

CCSS.HSN.VM.C.11

In the example of a transformation from R^3 to R^2, what is the result of multiplying matrix A by vector x?

• A matrix

• A vector in R^3

• A vector in R^2

• A scalar value

Tags

CCSS.HSN.VM.C.11

What is the dimension of the output vector in a transformation from R^3 to R^2?

• 1

• 2

• 4

• 3

In the example of a transformation from R^2 to R^3, what is the dimension of the resulting vector?

• 4

• 2

• 1

• 3

Tags

CCSS.HSN.VM.C.9

What is a linear transformation?

• A function that maps matrices to vectors

• A function that maps vectors to numbers

• A function that maps one vector space to another while preserving vector addition and scalar multiplication

• A function that maps numbers to vectors

Tags

CCSS.HSN.VM.C.9

Which property must a linear transformation satisfy?

• T(u + v) = T(u) - T(v)

• T(cu) = c + T(u)

• T(cu) = c - T(u)

• T(u + v) = T(u) + T(v)

Why is a matrix transformation considered a linear transformation?

• Because it maps vectors to numbers

• Because it maps numbers to matrices

• Because it satisfies the properties of vector addition and scalar multiplication

• Because it maps matrices to vectors