Step by Step Solver to Calculate the Determinant
of a 3 by 3 Matrix

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A step by step worksheet solver to calculate the determinant of a 3 by 3 matrix is presented. Unlimited number of practice questions can be generated along with their detailed solutions. Solve each step below then click on "Show me" to check your answer.

Step by step solution

STEP 1: - Write down the determinant $D$ of the 3 by 3 matrix.

STEP 2: - Write down the sign chart for a 3 by 3 determinant.

STEP 3: - Select any row or column and find its minors and cofactors. As an example, we select and work with the first row in the given matrix. Minors $M_{ij}$ are obtained by ignoring the row and column containing that elelemnt and calculating the determinant of the remaining smalller matrix. Cofactors $C_{ij}$ are obtained from minors using the sign chart shown in step 2: the cofator is equal to the minor mutliplied by the corresponding sign in the sign chart.

STEP 4: - Calculate the determinant D by multiplying each element in the first row by its cofactor found in step 2. Let $a_{11}$, $a_{12}$ and $a_{13}$ be the 3 elements making up the first row. The determinant of the given matrix is given by: $a_{11} \times C_{11}+ a_{12}\times a_{12} + a_{13}\times c_{13}$.