The given matrix equation is,
.
Multiplying the matrices with the scalars, the given equation becomes,
Adding the matrices,
Matrix equality gives,
Solving the equations together,
We can see that the equations are not consistent.
There is no solution.
Let us calculate the area of the walk.
Since the width of the walk is 3 feet, and the walk will be placed all the 4 sides,
Length of the plot including walk = 20 + (2 × 3) = 20 + 6 = 26 feet.
Breadth of the plot including walk = 30 + (2 × 3) = 36 feet.
Area of the plot including walk = 26 × 36 square feet.
Area of the plot = 20 × 30 square feet.
Area of the walk = (26 × 36) - (20 × 30)
= 936 - 600
= 336 square feet.
= square yards
= 37.3 square yards
Cost of the walk per square yard = $12.25.
Therefore, total cost of the walk = 12.25 × 37.3 = $456.92.