Haynes Boone
09/24/2024 · Junior High School
O 2.5.1 Obtención de las transpuestas de tres matrices e las transpuestas de las matrices \[ A=\left(\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right) \quad B=\left(\begin{array}{rrr}2 & 3 & 1 \\ -1 & 4 & 6\end{array}\right) \quad C=\left(\begin{array}{rrr}1 & 2 & -6 \\ 2 & -3 & 4 \\ 0 & 1 & 2 \\ 2 & -1 & 5\end{array}\right) \]
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Para obtener las transpuestas de las matrices \( A \), \( B \) y \( C \), simplemente intercambiamos filas por columnas. A continuación, se presentan las transpuestas de cada una de las matrices:
1. **Transpuesta de la matriz \( A \)**:
\[
A^T = \left(\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}\right)
\]
2. **Transpuesta de la matriz \( B \)**:
\[
B^T = \left(\begin{array}{rr} 2 & -1 \\ 3 & 4 \\ 1 & 6 \end{array}\right)
\]
3. **Transpuesta de la matriz \( C \)**:
\[
C^T = \left(\begin{array}{rrrr} 1 & 2 & 0 & 2 \\ 2 & -3 & 1 & -1 \\ -6 & 4 & 2 & 5 \end{array}\right)
\]
Así que las transpuestas de las matrices son:
- \( A^T = \left(\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}\right) \)
- \( B^T = \left(\begin{array}{rr} 2 & -1 \\ 3 & 4 \\ 1 & 6 \end{array}\right) \)
- \( C^T = \left(\begin{array}{rrrr} 1 & 2 & 0 & 2 \\ 2 & -3 & 1 & -1 \\ -6 & 4 & 2 & 5 \end{array}\right) \)
Quick Answer
Las transpuestas de las matrices son:
- \( A^T = \left(\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}\right) \)
- \( B^T = \left(\begin{array}{rr} 2 & -1 \\ 3 & 4 \\ 1 & 6 \end{array}\right) \)
- \( C^T = \left(\begin{array}{rrrr} 1 & 2 & 0 & 2 \\ 2 & -3 & 1 & -1 \\ -6 & 4 & 2 & 5 \end{array}\right) \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit