Directions: Use the following matrix to perform the elementary row operations sequentially.
A=[3 2 |8]
[5 2 |12]
1.) (1/3) R1 From the original matrix
2.) -5R1+R R2 From matrix in question 1.
1/3 R1 is [1 2/3 | 8/3]
-5R1 + R2 is
[-5 -10/3 | -40/3]
+[5 2 | 12]
= [0 -4/3 | 8/3]
If things are garbled, fix 'em.
To perform the operations, follow these steps:
1.) (1/3) R1 From the original matrix:
To multiply the first row by (1/3), simply divide each element of the row by 3:
A = [3 2 | 8]
[5 2 | 12]
Divide each element of the first row by 3:
A = [(3/3) (2/3) | (8/3)]
[5 2 | 12]
Simplify if necessary:
A = [1 (2/3) | (8/3)]
[5 2 | 12]
2.) -5R1 + R2 From matrix in question 1:
To perform this operation, multiply the first row by -5, and then add it to the second row:
A = [1 (2/3) | (8/3)]
[5 2 | 12]
Multiply each element of the first row by -5:
A = [-5*(-5) (-5*(2/3)) | (-5*(8/3))]
[5 2 | 12]
Simplify if necessary:
A = [25 (-10/3) | (-40/3)]
[5 2 | 12]
Next, add each corresponding element from the first row to the second row:
A = [25+5 (-10/3)+2 | (-40/3)+12]
[5 2 | 12]
Simplify if necessary:
A = [30 (-10/3)+2 | (-40/3)+12]
[5 2 | 12]
A = [30 (-4/3) | (4/3)]
[5 2 | 12]
So, after performing the given row operations, the updated matrix A is:
A = [30 (-4/3) | (4/3)]
[5 2 | 12]