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Published on October 17, 2025
Calculate and compare the fractional areas of two triangles within a rectangle, given the rectangle's total area is 1.
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The eigenvalues of the matrix [[3, 1], [1, 3]] are 4 and 2.
The eigenvalues of the matrix [[0, 1], [-1, 0]] are i and -i.
The eigenvalues of the given 3x3 matrix are 1, 2, and 2.
The determinant of the given 4x4 matrix is calculated using cofactor expansion along the fourth row, resulting in a determinant of -21.
The determinant of the 2x2 matrix [[2, 2], [3, 5]] is calculated as (2 * 5) - (2 * 3) = 4.
The determinant of the 3x3 matrix is calculated using the formula a(ei - fh) - b(di - fg) + c(dh - eg), resulting in a determinant of 0.