Matrix Operations: A Comprehensive Overview

What is a matrix?

• A single number

• A collection of variables

• An array of numbers arranged in rows and columns

• A type of equation

How is the order of a matrix defined?

• Columns by rows

• Rows by columns

• Sum of rows and columns

• Difference of rows and columns

When can two matrices be added or subtracted?

• When one is a scalar multiple of the other

• When they have the same number of rows

• When they have different dimensions

• When they have the same dimensions

What happens to the signs of a matrix when it is subtracted?

• They remain the same

• They flip

• They all become positive

• They all become negative

What is a scalar in the context of matrices?

• A matrix with one column

• A matrix with equal rows and columns

• A matrix with one row

• A single number

How do you perform scalar multiplication on a matrix?

• Add the scalar to each entry

• Subtract the scalar from each entry

• Multiply the scalar by each entry

• Divide each entry by the scalar

How do you solve a matrix equation for a variable?

• Multiply the matrices

• Subtract one matrix from the other and then divide by the scalar

• Transpose the matrices

• Add the matrices

What must be true for two matrices to be multiplied?

• They must have the same number of rows

• They must have the same number of columns

• They must be square matrices

• The number of columns in the first matrix must equal the number of rows in the second matrix

What is the resulting dimension of multiplying a 3x2 matrix with a 2x3 matrix?

• 3x2

• 2x2

• 3x3

• 2x3

Why is it not possible to multiply a 2x4 matrix with a 3x2 matrix?

• The matrices have different dimensions

• The number of rows in the first matrix does not match the number of columns in the second matrix

• The number of columns in the first matrix does not match the number of rows in the second matrix

• The matrices are not square