Matrix Transpose and Properties Quiz

What is the notation used to denote the transpose of a matrix A?

• A*

• A'

• A^T

• A^2

When finding the transpose of a matrix, what happens to the rows and columns?

• Rows become rows and columns become columns

• Rows and columns are deleted

• Rows remain rows and columns remain columns

• Rows become columns and columns become rows

If a matrix A is 3x2, what will be the dimensions of its transpose?

• 3x3

• 3x2

• 2x3

• 2x2

What is a symmetric matrix?

• A matrix with equal rows and columns

• A matrix with all zero entries

• A matrix that is equal to its own transpose

• A matrix with no transpose

What is the main diagonal of a matrix?

• The diagonal from the top left to the bottom right

• The diagonal from the top right to the bottom left

• The row with the most elements

• The column with the most elements

What property does a matrix have if it is equal to its transpose?

• Skew-symmetric

• Symmetric

• Diagonal

• Identity

How can you construct a symmetric matrix using a matrix B?

• Add B to its transpose

• Multiply B by its transpose

• Subtract B from its transpose

• Divide B by its transpose

What is the result of multiplying a matrix by its transpose?

• A diagonal matrix

• A zero matrix

• A symmetric matrix

• An identity matrix

When taking the transpose of a matrix product, what must be done with the component matrices?

• Take the transpose of each and reverse the order

• Add them together

• Subtract them

• Multiply them directly

If C is a matrix and E is another matrix, what is the transpose of their product CE?

• C^T E^T

• C + E

• E^T C^T

• CE