Project Using the Transformation

Problem

|[a,b,c],[d,e,ƒ],[g,h,i]|=8,|[a,b,c],[2*d+a,2*e+b,2*ƒ+c],[g,h,i]|

Solution

1. Identify the row operation performed on the original matrix to obtain the second matrix.

2. Observe that the second row (R_2) of the original matrix has been replaced by 2*(R_2)+(R_1)

3. Apply the property that adding a multiple of one row to another row does not change the value of the determinant.

4. Apply the property that multiplying a row by a scalar k multiplies the determinant by k

5. Decompose the operation into two steps: first, multiplying (R_2) by 2 which changes the determinant to 2×8=16

6. Note that adding (R_1) to this new row does not change the value further.

Final Answer

|[a,b,c],[2*d+a,2*e+b,2*ƒ+c],[g,h,i]|=16

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