Math Problem Statement
Jika |A^T| adlaah determinan dari A^T, hitunglah nilai |A| dan |A^T|. Buktikan |A|=|A^T|. a. |A|=|2 1 3 0 1 2 1 2 1| b. |A|=|1 2 -1 3 0 2 1 1 2|
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinants
Matrix Transposition
Formulas
|A| = |A^T| (Determinant of a matrix is equal to its transpose)
Determinant formula for 3x3 matrix using Sarrus' Rule: |A| = a(ei − fh) − b(di − fg) + c(dh − eg)
Theorems
Determinant of a matrix is equal to the determinant of its transpose
Sarrus' Rule for calculating determinants of 3x3 matrices
Suitable Grade Level
University Level (Linear Algebra)
Related Recommendation
Find Determinant of Matrix A and Evaluate (A^2 - B^T)C
How to Find Determinants of Matrices A, B, and AB: Verify |A||B| = |AB|
Matrix Determinant and Operations: Find Determinant of A and Evaluate (A^2 - B^T)C
Proof Using Properties of Determinants to Show Matrix A = [R1:b+c,a,bc and R2:b,c+a,b and R3:c,c,a+b] = 4abc
Express Matrix A and Calculate Determinant - Step-by-Step Guide