Math Problem Statement

Given the matrices A, B, and C, determine the following expressions: (3A - B) + 2A, 5A - (BA), (AB)^T C, C^T B, (2A)C - BC.

Solution

The image contains a matrix algebra problem. Here's a transcription of the problem:

Given: A=[4215],B=[1234],C=[213542]A = \begin{bmatrix} 4 & 2 \\ 1 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 2 \\ -3 & 4 \end{bmatrix}, \quad C = \begin{bmatrix} -2 & 1 & 3 \\ 5 & 4 & 2 \end{bmatrix}

Determine:

  1. (3AB)+2A(3A - B) + 2A
  2. 5A(BA)5A - (BA)
  3. (AB)TC(AB)^T C
  4. CTBC^T B
  5. (2A)CBC(2A)C - BC

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Matrix Multiplication
Matrix Transposition

Formulas

(3A - B) + 2A
5A - (BA)
(AB)^T C
C^T B
(2A)C - BC

Theorems

Matrix Addition and Subtraction
Matrix Multiplication
Transposition of Matrices

Suitable Grade Level

Grade 11-12 or Undergraduate