The value of 147258369 is :
Get the complete, step-by-step math solution for: "The value of 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 is :". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Define the Determinant
To find the determinant of a 3×3 matrix, we use the cofactor expansion method. We multiply each element of the first row by the determinant of its corresponding 2×2 submatrix, alternating signs.
Step 2: Substitute the values
Now, we substitute the given values into the determinant formula. We take the first element, 1, and multiply it by the determinant of the submatrix formed by removing its row and column. We do the same for 2 and 3, remembering to alternate the signs.
Step 3: Calculate the 2×2 determinants
Next, we calculate the determinants of the 2×2 submatrices. The determinant of a 2×2 matrix acbd is ad - bc.
Step 4: Simplify the expression
We perform the multiplications within each parenthesis to simplify the expression further.
Step 5: Perform the final calculations
Finally, we complete the arithmetic operations: multiplication, then addition and subtraction, to arrive at the determinant's value.