Math Problem Statement

(a)Calculatethedeterminantsofthefollowingmatrices, ifpossible(1p): A=   −2 1 3 1 0 3 0 1 3   (i) B= 3 4 2 −5 −6 −3 (ii) C=     2 3 6 −3 0 −2 −5 9 0 0 0 −4 0 0 0 1    . (iii) (b)Whichofthematricesfrompart(a)haveaninversematrix? (c)Forwhichsystemsofequationscorrespondingtothematricesinpart(a)isthesolution unique?

Solution

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Math Problem Analysis

Mathematical Concepts

Matrix Determinants
Inverse Matrices
Systems of Linear Equations

Formulas

Determinant of a 3x3 matrix: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
Determinant of a 4x4 matrix using cofactor expansion

Theorems

A matrix has an inverse if and only if its determinant is non-zero
A system of equations has a unique solution if the corresponding matrix is square and has a non-zero determinant

Suitable Grade Level

Grades 11-12 or College Level