Question
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Answer
The determinant of matrix A is 8.
Solution
-
Recall that the determinant of a
matrix is given by -
For the matrixidentify the values:
-
Compute the product
: -
Compute the product
: -
Calculate the determinant:
Thus, the determinant of
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To find the determinant of matrix
where
Thus, the answer is (a) 8.
For a bit of historical fun, did you know that determinants were first introduced in the 17th century? Mathematicians like Leibniz and Cramer helped lay the foundation for this important concept in linear algebra, which is now indispensable in fields from physics to computer science!
In terms of real-world application, determinants are pivotal in solving systems of linear equations. For instance, in engineering, they help determine system stability and in computer graphics, they assist in transformations like rotations and scaling of images—imagine how 3D graphics rely on matrices for rendering smooth animations!
