Matrices Flashcard for Adv. Alg.

Front

What are the dimensions of the product of a (4x33) matrix A and a (33x1) matrix B?

Back

4x1

Front

What is the result of multiplying the following matrices: \[ \begin{pmatrix} 20 & 15 & -10 \ 30 & -5 & 0 \ \end{pmatrix} \begin{pmatrix} 1 \ 8 \ 3 \ \end{pmatrix} \]?

Back

\[ \begin{pmatrix} -20 & 15 & -10 \ 30 & -5 & 0 \ \end{pmatrix} \]

Front

What is the result of adding the following matrices: \[ \begin{pmatrix} 11 & 8 \ -4 & 2 \ \end{pmatrix} + \begin{pmatrix} 3 & 2 \ -6 & -6 \ \end{pmatrix} \]?

Back

\[ \begin{pmatrix} 11 & 8 \ -4 & 2 \ \end{pmatrix} \]

Front

What is the result of finding B*A if B is a (33x1) matrix and A is a (4x33) matrix?

Back

Not possible because rows do not match columns.

Front

What is the result of subtracting the following matrices: \[ \begin{pmatrix} -5 \end{pmatrix} - \begin{pmatrix} 8 \end{pmatrix} \]?

Back

-9

Front

Define a matrix.

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What is the identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is the determinant of a 2x2 matrix \[ \begin{pmatrix} a & b \ c & d \ \end{pmatrix} \]?

Back

The determinant is calculated as \( ad - bc \).

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix B such that \( AB = BA = I \), where I is the identity matrix.

Front

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each entry of a matrix by a scalar (a constant).