https://file.aiquickdraw.com/mathbot/file/1726621487997cq80quc0.jpg

Let's break down the problem based on the image. The matrices given are:

\[
A = \begin{bmatrix} 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & -3 \\ -1 & 5 \end{bmatrix}, \quad C = \begin{bmatrix} 6 & 4 & 0 \\ 8 & 2 & -10 \end{bmatrix}
\]
\[
D = \begin{bmatrix} 3 & 5 \\ 1 & 2 \\ 0 & -4 \end{bmatrix}, \quad E = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 3 & 4 \\ 1 & 2 & 3 \end{bmatrix}
\]

The tasks are:

1. **Calculate \( C + D^T \)** where \( D^T \) is the transpose of matrix \( D \).
2. **Scalar multiplication \( \frac{1}{3} C \)**.
3. **Matrix multiplication \( AB \)**.
4. **Find the inverse of matrix \( B \), \( B^{-1} \)**.
5. **Calculate the determinant of matrix \( E \)**.

Let me go step by step and solve these.Here are the solutions for the given tasks:

1. **\( C + D^T \)**:
   \[
   \begin{bmatrix} 9 & 5 & 0 \\ 13 & 4 & -14 \end{bmatrix}
   \]

2. **\( \frac{1}{3} C \)**:
   \[
   \begin{bmatrix} 2 & 1.33 & 0 \\ 2.67 & 0.67 & -3.33 \end{bmatrix}
   \]

3. **Matrix multiplication \( AB \)**:
   \[
   \begin{bmatrix} 0 & 7 \end{bmatrix}
   \]

4. **Inverse of matrix \( B \), \( B^{-1} \)**:
   \[
   \begin{bmatrix} 0.71 & 0.43 \\ 0.14 & 0.29 \end{bmatrix}
   \]

5. **Determinant of matrix \( E \)**:
   \[
   \text{Determinant of } E = -2.0
   \]

Let me know if you'd like further explanation or details on any part of this. 

### Related questions:
1. What are the properties of the transpose of a matrix?
2. How does scalar multiplication affect each element of a matrix?
3. Why does the inverse of a matrix matter, and how is it calculated?
4. What does the determinant of a matrix signify geometrically?
5. How can matrix multiplication be interpreted in terms of linear transformations?

### Tip:
Always verify if a matrix is invertible by checking if its determinant is non-zero before calculating the inverse.

Perhatikan matriks berikut: A=[1 2], B=[[2 -3],[-1 5]], C=[[6 4 0],[8 2 -10]], D=[[3 5],[1 2],[0 -4]], E=[[1 2 1],[2 3 4],[1 2 3]]. Maka tentukan: 1. Hasil dari matriks C + DT adalah... 2. Hasil dari perkalian skalar 1/3 C adalah... 3. Hasil perkalian matriks AB adalah... 4. Nilai invers matriks B-1 adalah... 5. Determinan matriks E adalah...

This problem involves matrix operations including matrix addition, scalar multiplication, matrix multiplication, inverse calculation, and finding the determinant. Suitable for advanced math students, this exercise covers topics like matrix transpose, inverses, and determinants for matrices A, B, C, D, and E.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation