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 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: $a_{11} \times C_{11}+ a_{12}\times a_{12} + a_{13}\times c_{13}$. |
