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Exercises Systems of equations

Example 8 from Algebra and Trigonometry, 11.5 Matrices and Matrix Operations

Multiplying Two Matrices

Multiply matrix $A$ and matrix $B .$

A = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] and B = [\begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix}]

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, we check the dimensions of the matrices. Matrix $A$ has dimensions $2 \times 2$ and matrix $B$ has dimensions $2 \times 2.$ The inner dimensions are the same so we can perform the multiplication. The product will have the dimensions $2 \times 2.$
We perform the operations outlined previously.

How did it go?

PreviousFinding the Sum of Scalar Multiples Next Multiplying Two Matrices

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.