Math Problem Statement

Tentukan Invers Matriks B

Solution

The image appears to contain a mathematical problem in Indonesian, asking for the inverse of matrix BB. The matrices provided are:

A=(012341025),B=(143121)A = \begin{pmatrix} 0 & 1 & -2 \\ 3 & 4 & 1 \\ 0 & 2 & 5 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 4 \\ 3 & 1 \\ 2 & 1 \end{pmatrix}

The problem specifically asks to find the inverse of matrix BB.

Let's calculate the inverse of matrix BB, if it exists. To do that, the matrix must be square (having the same number of rows and columns). However, matrix BB is 3×23 \times 2, which means it's not square, and therefore, it doesn't have an inverse.

Would you like assistance with a different part of the problem or clarification on another topic related to matrices?

Here are some related questions you might find helpful:

  1. What conditions are necessary for a matrix to have an inverse?
  2. How do you find the inverse of a square matrix?
  3. What is the determinant of a matrix and how does it relate to the inverse?
  4. How do you perform matrix multiplication?
  5. Can a non-square matrix have a pseudoinverse?

Tip: When working with matrix inverses, always ensure that the matrix is square, as only square matrices can have a true inverse!

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Math Problem Analysis

Mathematical Concepts

Matrix Inversion
Linear Algebra

Formulas

Inverse of a Matrix
Condition for a matrix to have an inverse

Theorems

A matrix has an inverse if it is square and its determinant is non-zero

Suitable Grade Level

Grades 10-12