Transpose and inverse in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the transpose of a matrix do?

The transpose flips a matrix over its diagonal, turning rows into columns and columns into rows.

beginner

How do you find the transpose of a matrix in R?

Use the function t(). For example, t(matrix) returns the transpose of matrix.

beginner

What is the inverse of a matrix?

The inverse of a matrix is another matrix that, when multiplied with the original, gives the identity matrix. It 'undoes' the effect of the original matrix.

beginner

How do you calculate the inverse of a matrix in R?

Use the function solve(). For example, solve(matrix) returns the inverse of matrix if it exists.

intermediate

What happens if you try to invert a matrix that is not invertible?

R will give an error because the inverse does not exist. Such matrices are called singular or non-invertible.

Which R function is used to get the transpose of a matrix?

A inv()

B transpose()

C solve()

D t()

The function t() returns the transpose of a matrix in R.

What does the inverse of a matrix multiplied by the original matrix produce?

A Zero matrix

B Diagonal matrix

C Identity matrix

D Transpose matrix

Multiplying a matrix by its inverse results in the identity matrix.

Which function in R calculates the inverse of a matrix?

A t()

B solve()

C inv()

D inverse()

The solve() function computes the inverse of a matrix in R.

If a matrix is singular, what happens when you try to invert it in R?

A Gives an error

B Returns zero matrix

C Returns the original matrix

D Returns identity matrix

Trying to invert a singular matrix causes an error because the inverse does not exist.

What is the result of transposing a 3x2 matrix?

A 2x3 matrix

B 3x2 matrix

C 2x2 matrix

D 3x3 matrix

Transposing swaps rows and columns, so a 3x2 matrix becomes 2x3.

Explain how to find the transpose and inverse of a matrix in R, including what functions to use and what the results mean.

Think about flipping rows and columns for transpose, and undoing matrix multiplication for inverse.

Describe what happens when you try to invert a matrix that is not invertible in R and why.

Consider what it means for a matrix to have no inverse.