MATH1503 Study Guide - Final Guide: Linear Map, Invertible Matrix, Parallelepiped
Document Summary
Describe how to use determinants to find areas of triangles and parallelograms, and volumes of parallelepipeds. In order to find the area of a triangle with determinants, multiply the the absolute value of the determinant of the matrix made up by the triangle"s vertices by . In order to find the area of a parallelogram with determinants, take the absolute value of the determinant of the matrix formed from the vectors of the parallelogram. In order to find the area of parallelepipeds with determinants, take the absolute value of the determinant of the matrix formed by the vectors of the parallelepiped. Give the formula for finding the determinant of a matrix by expanding across a given row or down a given column. Expanding across a given row i: det a = ai1ci1 + ai2ci2 + + aincin. Expanding down a given column j: det a = a1jc1j + a2jc2j + + anjcnj.
