Math Problem Statement

2 question

The image contains problems related to matrix operations and determinant calculations. It includes tasks to compute matrix expressions and find determinants.

Solution

The image you uploaded contains the following mathematical problems:

  1. Matrix Operations: You are asked to compute the expression 3AT+2AB3A^T + 2AB, where:

    • A=(876210)A = \begin{pmatrix} 8 & 7 & 6 \\ 2 & 1 & 0 \end{pmatrix}
    • B=(123456789)B = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}
  2. Determinant Calculation: You are asked to calculate the determinant of the matrix:

    -6 & -8 & 3 \\ 4 & -3 & -1 \end{pmatrix}$$

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Math Problem Analysis

Mathematical Concepts

Matrix Operations
Determinants
Linear Algebra

Formulas

Matrix Transpose
Matrix Multiplication
Determinant of a Matrix

Theorems

Properties of Determinants
Matrix Multiplication Rules

Suitable Grade Level

Grades 11-12, College