Question Video: Identifying a Pair of Simultaneous Equations from a Matrix Equation Mathematics

Write down the set of simultaneous equations that could be solved using the given matrix equation. [3, 3 and 2, 4][𝑎 and 𝑏] = [10 and 12]

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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.

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