Wheeler Brooks
02/08/2024 · Primary School
\( A=\left(\begin{array}{ccc}0 & -1 & 2 \\ 3 & 4 & 5 \\ 8 & -7 & 6\end{array}\right), k=3 \). Найти: \( k \cdot A \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Чтобы найти \( k \cdot A \), нужно умножить каждую элемент матрицы \( A \) на число \( k \).
Дана матрица \( A \):
\[
A = \begin{pmatrix}
0 & -1 & 2 \\
3 & 4 & 5 \\
8 & -7 & 6
\end{pmatrix}
\]
Умножим матрицу \( A \) на \( k = 3 \):
\[
k \cdot A = 3 \cdot \begin{pmatrix}
0 & -1 & 2 \\
3 & 4 & 5 \\
8 & -7 & 6
\end{pmatrix} = \begin{pmatrix}
3 \cdot 0 & 3 \cdot (-1) & 3 \cdot 2 \\
3 \cdot 3 & 3 \cdot 4 & 3 \cdot 5 \\
3 \cdot 8 & 3 \cdot (-7) & 3 \cdot 6
\end{pmatrix}
\]
Теперь вычислим каждое значение:
\[
= \begin{pmatrix}
0 & -3 & 6 \\
9 & 12 & 15 \\
24 & -21 & 18
\end{pmatrix}
\]
Таким образом, результатом будет:
\[
k \cdot A = \begin{pmatrix}
0 & -3 & 6 \\
9 & 12 & 15 \\
24 & -21 & 18
\end{pmatrix}
\]
Quick Answer
Результат умножения матрицы \( A \) на \( k = 3 \) будет:
\[
k \cdot A = \begin{pmatrix}
0 & -3 & 6 \\
9 & 12 & 15 \\
24 & -21 & 18
\end{pmatrix}
\]
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