Let A =


1 0
0 1
0
0
1 3 4

 =
[ A11 A12
A21 A22
]
and B =


1
2
0
0
3 4

 =
[ B11 B12
B21 B22
]
.
(a) Find (i) A11B11 + A12B21, (ii) A11B12 + A12B22, (iii) A21B11 + A22B21, (iv)A21B12 + A22B22
(b) Find AB using your work from part (a)

Given the matrices \( A \) and \( B \), we are asked to perform matrix multiplication and compute specific products.

### Matrices:
Matrix \( A \) is given as:
\[
A = 
\begin{bmatrix}
1 & 0 \\
0 & 1 \\
0 & 1 \\
1 & 3 & 4
\end{bmatrix}
= 
\begin{bmatrix}
A_{11} & A_{12} \\
A_{21} & A_{22}
\end{bmatrix}
\]
Where:
- \( A_{11} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \)
- \( A_{12} = \begin{bmatrix} 0 \\ 1 \end{bmatrix} \)
- \( A_{21} = \begin{bmatrix} 0 & 1 \end{bmatrix} \)
- \( A_{22} = \begin{bmatrix} 3 & 4 \end{bmatrix} \)

Matrix \( B \) is given as:
\[
B = 
\begin{bmatrix}
1 & 2 \\
0 & 0 \\
0 & 3 & 4
\end{bmatrix}
= 
\begin{bmatrix}
B_{11} & B_{12} \\
B_{21} & B_{22}
\end{bmatrix}
\]
Where:
- \( B_{11} = \begin{bmatrix} 1 & 2 \\ 0 & 3 & 4 \end{bmatrix}
The products based on your child

Let A = [1 0; 0 1; 0; 0; 1 3 4] = [A11 A12; A21 A22] and B = [1; 2; 0; 0; 3 4] = [B11 B12; B21 B22]. (a) Find (i) A11B11 + A12B21, (ii) A11B12 + A12B22, (iii) A21B11 + A22B21, (iv) A21B12 + A22B22. (b) Find AB using your work from part (a).

Explore the step-by-step solution to matrix multiplication involving block matrices A and B. This problem covers essential concepts of linear algebra, including block matrix partitioning and multiplication rules. Ideal for college-level mathematics students.

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