We used Gaussian elimination on matrix X to find its determi

We used Gaussian elimination on matrix X to find its determinant. Below are the 3 steps we applied: Step 1: -r1 + 2r3 r1 Step 2: Step 3: -210 r3 + 5T2 r2 Calculate det(X) we call this new matrix D, and we know det(D)-100

Solution

Steps to calculate Gaussian Elimination det(X)

1) Swapping two rows or columns will given Det(A) = (-1) Det (A)

2) If we factor out the number from the rows or columns, then Det(A) = k^n Det(A)

3) Adding subtraction one row to multiple of one another row => Det(A)

a) Last step will increase the matrix determinant to 3^{5}

Dold * 3^{5} = 20

Dold = 20/243

Swapping r2 and r3, we get the determinant as negative

Dold1 = -20/243

Dnew1 = 20/243

Hence the final determinant is equal to 20/243 so therefore det(X) = 20/243

b)

Making -2r3 + 10r1 ---> r1, we get

Dold1 = 20/3^10

Dold2 = -20/3^10

Dold3 = -20/3^5

Dold4 = 20/3^5

Dold 5 = -20/3^5

Hence the det(X) = -20/243