For the given matrices A and B, Fill up the blank on C=AB by using Partitioning matrices method. ONLY USE REQUIRED PART OF A AND B TO COMPUTE THE MISSING PART ON C! NOT THE WHLE A AND B MATRICES! A= C = 1 2 2 3 5 3 1 >> C=A*B 24 28 33 34 -1 1 3-1 2 3 2 26 38 2 4 5 27 4 4 6 6 7 42 54 and 2 B = 1 48 33 11 74 79 2 1 5 1 2 40 5 42 54 3 4 3 2 4 2 3 5 4 -1
For the given matrices A and B, Fill up the blank on C=AB by using Partitioning matrices method. ONLY USE REQUIRED PART OF A AND B TO COMPUTE THE MISSING PART ON C! NOT THE WHLE A AND B MATRICES! A= C = 1 2 2 3 5 3 1 >> C=A*B 24 28 33 34 -1 1 3-1 2 3 2 26 38 2 4 5 27 4 4 6 6 7 42 54 and 2 B = 1 48 33 11 74 79 2 1 5 1 2 40 5 42 54 3 4 3 2 4 2 3 5 4 -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Matrix Multiplication Using Partitioning Matrices Method**
**Problem Statement:**
For the given matrices \( A \) and \( B \), fill up the blank on \( C = AB \) by using the Partitioning Matrices method.
**Note:**
- Only use the required part of matrices \( A \) and \( B \) to compute the missing part of matrix \( C \).
- Do not use the entire matrices \( A \) and \( B \).
**Given Matrices:**
\[
A = \begin{pmatrix}
2 & 1 & 3 & 4 & -1 \\
1 & 2 & -1 & 1 & 4 \\
3 & 1 & 2 & 1 & 1 \\
-5 & -1 & 4 & 7 & 2 \\
-1 & 2 & 1 & -4 & 6
\end{pmatrix}
\]
\[
B = \begin{pmatrix}
1 & 2 & 3 & 4 \\
1 & 2 & 1 & 3 \\
2 & 1 & 2 & 5 \\
3 & 2 & 1 & 2 \\
4 & 2 & 6 & 1
\end{pmatrix}
\]
**Solution:**
Using the partitioning matrices method, we need to find the missing elements of matrix \( C \):
\[
C = A * B
\]
Given partial matrix \( C \):
\[
C = \begin{pmatrix}
48 & 40 & & \\
33 & 5 & & \\
24 & 26 & 42 & \\
28 & 38 & 54 & \\
33 & 34 & 42 & \\
33 & 74 & 79 & 54
\end{pmatrix}
\]
**Method:**
To find the missing parts of matrix \( C \), we need to multiply the relevant parts of matrices \( A \) and \( B \).
Calculate:
- For \( c_{1, 1} \), \( c_{1, 2} \)
\[
c_{1, 1} = 2*1 + 1*1 + 3*2 + 4*3 + (-1)*4 = 48
\]
\[
c_{1, 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecd9d238-92a1-4a47-af9e-c758e887edd1%2Fe5690a22-fe5e-4fe3-bf55-a61f1308cdd0%2Fdqsl36g_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplication Using Partitioning Matrices Method**
**Problem Statement:**
For the given matrices \( A \) and \( B \), fill up the blank on \( C = AB \) by using the Partitioning Matrices method.
**Note:**
- Only use the required part of matrices \( A \) and \( B \) to compute the missing part of matrix \( C \).
- Do not use the entire matrices \( A \) and \( B \).
**Given Matrices:**
\[
A = \begin{pmatrix}
2 & 1 & 3 & 4 & -1 \\
1 & 2 & -1 & 1 & 4 \\
3 & 1 & 2 & 1 & 1 \\
-5 & -1 & 4 & 7 & 2 \\
-1 & 2 & 1 & -4 & 6
\end{pmatrix}
\]
\[
B = \begin{pmatrix}
1 & 2 & 3 & 4 \\
1 & 2 & 1 & 3 \\
2 & 1 & 2 & 5 \\
3 & 2 & 1 & 2 \\
4 & 2 & 6 & 1
\end{pmatrix}
\]
**Solution:**
Using the partitioning matrices method, we need to find the missing elements of matrix \( C \):
\[
C = A * B
\]
Given partial matrix \( C \):
\[
C = \begin{pmatrix}
48 & 40 & & \\
33 & 5 & & \\
24 & 26 & 42 & \\
28 & 38 & 54 & \\
33 & 34 & 42 & \\
33 & 74 & 79 & 54
\end{pmatrix}
\]
**Method:**
To find the missing parts of matrix \( C \), we need to multiply the relevant parts of matrices \( A \) and \( B \).
Calculate:
- For \( c_{1, 1} \), \( c_{1, 2} \)
\[
c_{1, 1} = 2*1 + 1*1 + 3*2 + 4*3 + (-1)*4 = 48
\]
\[
c_{1, 2
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Step 1: Determining the matrices A and B
VIEWStep 2: Calculation of the elements in the first row C11,C12,C13
VIEWStep 3: Calculation of the elements in the second row C21,C22,C23
VIEWStep 4: Calculation of the elements in third and fourth rows C34,C35,C44,C45
VIEWStep 5: Calculation of the elements in the fifth and sixth rows C52,C53,C62,C63
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