Write down the set of simultaneous
equations that could be solved using the given matrix equation, that is, where the
two-by-two matrix with elements three, three, two, four multiplied by the column
matrix with elements 𝑎, 𝑏 is equal to the column matrix with elements 10, 12.
We’re given a matrix equation of
the form 𝐴𝑋 is equal to 𝐵. That’s where 𝐴 is the matrix of
coefficients, the coefficient matrix; 𝑋 is the variable matrix, that’s the matrix
of unknowns; and 𝐵, the matrix on the right-hand side, is the constant matrix.
Now, in order to recover the set of
simultaneous equations that could be solved using the matrix equation given, we need
to multiply the coefficient matrix 𝐴 by the variable matrix 𝑋. We then equate each line of our
result with the appropriate line of the matrix 𝐵. So now let’s multiply out our
left-hand side. Multiplying our first row with the
column matrix 𝑎, 𝑏, we have three times 𝑎 plus three 𝑏. And equating to the first row in
our column matrix 𝐵, that’s equal to 10.
Next, we multiply our second row by
our column matrix 𝑋. And we have two multiplied by 𝑎
plus four multiplied by 𝑏. And this equates to the element in
the second row of matrix 𝐵, which is 12.
The set of simultaneous equations
that could be solved using the given matrix equation is therefore three 𝑎 plus
three 𝑏 is equal to 10 and two 𝑎 plus four 𝑏 is equal to 12.