Pregunta
1) Fill in the missing numbers. \( \left[\begin{array}{cc}2 & 8 \\ -3 & 2 \\ 0 & -9\end{array}\right]-\left[\begin{array}{rr}5 & 6 \\ 5 & 3 \\ 9 & 0\end{array}\right]=\left[\begin{array}{ll}\square \\ \square \\ \square & \square\end{array}\right. \)
Ask by Pearson Johnson. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\[
\left[\begin{array}{cc}
-3 & 2 \\
-8 & -1 \\
-9 & -9
\end{array}\right]
\]
Solución
To solve the matrix subtraction problem, we'll subtract the corresponding elements of the two matrices.
Given:
\[
\begin{array}{cc}
2 & 8 \\
-3 & 2 \\
0 & -9
\end{array}
-
\begin{array}{cc}
5 & 6 \\
5 & 3 \\
9 & 0
\end{array}
=
\begin{array}{cc}
\square & \square \\
\square & \square \\
\square & \square
\end{array}
\]
**Step-by-Step Subtraction:**
1. **First Row:**
\[
2 - 5 = -3 \\
8 - 6 = 2
\]
So, the first row of the result is \([-3 \quad 2]\).
2. **Second Row:**
\[
-3 - 5 = -8 \\
2 - 3 = -1
\]
So, the second row of the result is \([-8 \quad -1]\).
3. **Third Row:**
\[
0 - 9 = -9 \\
-9 - 0 = -9
\]
So, the third row of the result is \([-9 \quad -9]\).
**Final Result:**
\[
\begin{array}{cc}
-3 & 2 \\
-8 & -1 \\
-9 & -9
\end{array}
\]
Or, using the matrix notation:
\[
\left[\begin{array}{cc}
-3 & 2 \\
-8 & -1 \\
-9 & -9
\end{array}\right]
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Bonus Knowledge
To find the missing numbers in the matrix subtraction, we simply subtract the corresponding elements of the two matrices. For the first row: \(2 - 5 = -3\) and \(8 - 6 = 2\). For the second row: \(-3 - 5 = -8\) and \(2 - 3 = -1\). For the third row: \(0 - 9 = -9\) and \(-9 - 0 = -9\). So we can fill in the matrix as follows: \[ \left[\begin{array}{cc} -3 & 2 \\ -8 & -1 \\ -9 & -9 \end{array}\right] \]
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