Two welders worked a total of 47 h on a project. One welder made $37/h, while the other made $39/h. If the gross earnings of the two welders was $1781 for the job, how many hours did each welder work? Using row- echron matrix.

Question

Deegan Mullen · Accepted Answer

Step 1  Solving a system of equations using row-echlon form can be done by reducing the given matrix to another matrix, using transformations, such that each entry below the diagonal element of each column is 0.  Step 2  Let the two welders work for x and y hours respectively. As the total hours for which the two welders work is 47, hence we will have:  x+y=47 (i)  Also, the welders earn at a rate of 37 h and 39 h respectively and their gross earning was $1781. Hence we will have:   37x+39y=1781 (ii)  Thus we have a system of two linear equations which can be transformed to the matrix form as shown below:   [113738](xy)=[471781]  We can solve this system of equations by transforming it into a row-echlon form as shown below:   [113739](xy)=[471781]  R2→R2−37R1  [1102](xy)=[4742]  Note: Here we already obtain the row−echlon form and can use it to find the required values of x and y, but we go a step further and completelpy convert the matrix into an identity matrix to directly obtain the required values.  R2→12R2  [1101](xy)=[4721]  R1→R1−R2  [1001](xy)=[2621]  Thus we get the solution as, x=26 and y=21. Hence, the welders work for 26 hrs and 21 hrs respectively.

Two welders worked a total of 47 h on a

Answered question

Answer & Explanation

New Questions in Linear algebra