Math Problem Statement

Solve the following system of linear equations using matrices as well as Cramer's rule: 2x - y + z = 4 4x + 2y - 3z = 5 3x - 4y - z = 8

Solution

The image contains mathematical questions involving systems of linear equations and differentiation problems. I'll break down the questions visible in the image for better clarity:

  1. Question 2(b): Solve the following system of linear equations using matrices and Cramer's Rule: 2xy+z=42x - y + z = 4 4x+2y3z=54x + 2y - 3z = 5 3x4yz=83x - 4y - z = 8

  2. Question 2(i): Find f(x),f(x),f(x), f'(x), and f(x)f''(x) if: f(x)=ln(x2+4x+3)f(x) = \ln(x^2 + 4x + 3)

  3. Question 2(ii): Given: f(x)=15x2+25x+3f(x) = \frac{15}{x^2 + 25x + 3} Find f(x)f'(x).

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Systems of Equations
Cramer's Rule
Matrix Operations

Formulas

Cramer's rule: x = Dx/D, y = Dy/D, z = Dz/D
Determinant of 3x3 matrices

Theorems

Cramer's Theorem

Suitable Grade Level

Undergraduate Mathematics or Advanced High School (Grades 11-12)