Matrices | Algebra | BitWithBite

01 Key Concepts

Matrix Dimensions

A matrix with m rows and n columns is called an 'm by n' matrix. Example: a 2x3 matrix has 2 rows and 3 columns.

Matrix Addition and Subtraction

Add or subtract matrices of the same dimensions by combining their corresponding entries (same row, same column).

Scalar Multiplication

Multiply every entry in a matrix by the same single number (a scalar).

Matrix Multiplication

To multiply two matrices, the number of columns in the first must equal the number of rows in the second; each entry in the result comes from multiplying and summing a row from the first by a column from the second.

Identity Matrix

A square matrix with 1s on the main diagonal and 0s everywhere else; multiplying any matrix by the identity matrix leaves it unchanged.

02 Solved Examples

Example 1 Add the matrices [[1,2],[3,4]] and [[5,6],[7,8]].

Add corresponding entries: top-left: 1+5=6. top-right: 2+6=8.
bottom-left: 3+7=10. bottom-right: 4+8=12.

Answer: [[6,8],[10,12]]

Example 2 Multiply the matrix [[1,2],[3,4]] by the scalar 3.

Multiply every entry by 3: 1*3=3, 2*3=6, 3*3=9, 4*3=12.

Answer: [[3,6],[9,12]]

Example 3 Find the dimensions of a matrix with 3 rows and 5 columns.

State rows first, then columns, following the 'm by n' convention.

Answer: 3x5 (a 3 by 5 matrix)

03 Practice Questions

1Add [[1,0],[0,1]] and [[2,3],[4,5]].

[[3,3],[4,6]]

2Multiply [[2,4],[6,8]] by scalar 2.

[[4,8],[12,16]]

3Find the dimensions of a matrix with 4 rows and 2 columns.

4x2

4Subtract [[5,6],[7,8]] - [[1,1],[1,1]].

[[4,5],[6,7]]

5What does the identity matrix do when multiplying another matrix?

Leaves the matrix unchanged

📄 Matrices — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet