Let $$ \mathbf{A}=\left[\begin{array}{ll}1 & 1 \ 0 & 1\end{array} ight] $$ and $$ \mathbf{B}=\left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array} ight] $$ Identify $$ \mathbf{A} \odot \mathbf{B} $$.

Question

Let $$ \mathbf{A}=\left[\begin{array}{ll}1 & 1 \ 0 & 1\end{array}ight] $$ and $$ \mathbf{B}=\left[\begin{array}{ll}0 & 1 \ 1 & 0\end{array}ight] $$ Identify $$ \mathbf{A} \odot \mathbf{B} $$.

UpStudy AI · Accepted Answer

We are given
$$
\mathbf{A}=\begin{bmatrix}1 & 1 \ 0 & 1\end{bmatrix} \quad \text{and} \quad \mathbf{B}=\begin{bmatrix}0 & 1 \ 1 & 0\end{bmatrix},
$$
and the symbol $$\odot$$ denotes the Hadamard (entrywise) product. This product is defined by
$$
(\mathbf{A} \odot \mathbf{B})_{ij} = \mathbf{A}_{ij}\cdot \mathbf{B}_{ij}.
$$

**Step 1:** Multiply corresponding entries of $$\mathbf{A}$$ and $$\mathbf{B}$$.

- For the $$(1,1)$$ entry:
  $$
  1 \cdot 0 = 0.
  $$
  
- For the $$(1,2)$$ entry:
  $$
  1 \cdot 1 = 1.
  $$
  
- For the $$(2,1)$$ entry:
  $$
  0 \cdot 1 = 0.
  $$
  
- For the $$(2,2)$$ entry:
  $$
  1 \cdot 0 = 0.
  $$

**Step 2:** Write the resulting matrix.

Thus,
$$
\mathbf{A} \odot \mathbf{B} = \begin{bmatrix}0 & 1 \ 0 & 0\end{bmatrix}.
$$
$$ \mathbf{A} \odot \mathbf{B} = \begin{bmatrix}0 & 1 \ 0 & 0\end{bmatrix} $$

Let \( \mathbf{A}=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] \) and \( \mathbf{B}=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \) Identify \( \mathbf{A} \odot \mathbf{B} \).

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