Question

determinants
1/3/3
-1//6 3/2

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Answer 1

Answer:

Step-by-step explanation:

The Formula of the Determinant of 3×3 Matrix

The standard formula to find the determinant of a 3×3 matrix is a break down of smaller 2×2 determinant problems which are very easy to handle. If you need a refresher, check out my other lesson on how to find the determinant of a 2×2. Suppose we are given a square matrix AA where,

Matrix A is a square matrix with a dimension of 3x3 wherein the first row contains the elements a,b, and c; the second row contains the elements d, e, and f; and finally, the third row contains in the entries g, h, and i. In short form, matrix A can be expressed as A = [a,b,c;d,e,f;g,h,i].

The determinant of matrix A is calculated as

The determinant of matrix A = [a,b,c;d,e,f;g,h,i] is calculated as determinant of A = det(A) = det [a,b,c;d,e,f;g,h,i] = a times determinant of matrix [e,f;h,] minus b times determinant of matrix [d,f;g,i] + c times determinant of [d,e;g,h].

Here are the key points:

Notice that the top row elements namely aa, bb and cc serve as scalar multipliers to a corresponding 2-by-2 matrix.

The scalar aa is being multiplied to the 2×2 matrix of left-over elements created when vertical and horizontal line segments are drawn passing through aa.

The same process is applied to construct the 2×2 matrices for scalar multipliers bb and cc.

Determinant of 3 x 3 Matrix (animated)

This is an animated GIF file that shows the step-by-step procedure how to find the determinant of a 3 by 3 matrix with entries a, b, and c on its first row; entries d, e and f on its second row; and entries g, h, and i on its third row. The formula is det(A) = det[a,b,c;d,e,f;g,h,i] = a * det [e,f;h,i] - b * det [d,f;g,i] + c * det [d,e;g,h].

Examples of How to Find the Determinant of a 3×3 Matrix