### Video Transcript

Write down the set of simultaneous
equations that could be solved using the given matrix equation. Three, three, two, four multiplied
by 𝑎, 𝑏 is equal to 10, 12.

In order to answer this question,
we need to perform matrix multiplication. We begin by multiplying the
elements in the first row of the coefficient matrix by the elements in the column
variable matrix. Three multiplied by 𝑎 is equal to
three 𝑎, and three multiplied by 𝑏 is equal to three 𝑏. The sum of these terms will be
equal to the element in the first row of the constant matrix. This gives us the equation three 𝑎
plus three 𝑏 is equal to 10.

We then repeat this process for the
second row of the coefficient matrix. Two multiplied by 𝑎 is two 𝑎, and
four multiplied by 𝑏 is four 𝑏. This gives us the equation two 𝑎
plus four 𝑏 is equal to 12. We now have a set of simultaneous
equations that could be solved. Three 𝑎 plus three 𝑏 is equal to
10, and two 𝑎 plus four 𝑏 equals 12. Whilst we do not need to solve the
equations in this video, we could do so using the elimination or substitution
methods.