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    "# Mechanica"
   ]
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    "\n",
    "### Quiz Notations and Products\n",
    "\n",
    ":::{card} Exercise 1\n",
    "What is the type of the result of the product?\n",
    "\n",
    "$\\mathit{v}_i \\cdot \\mathit{A}_{ij} \\cdot \\mathit{w}_j$\n",
    "\n",
    "\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "Scalar\n",
    "```\n",
    ":::\n",
    "\n",
    ":::{card} Exercise 2\n",
    "How would you write the product\n",
    "\n",
    "$\\mathit{v}_i \\cdot \\mathit{A}_{ij} \\cdot \\mathit{w}_j$\n",
    "\n",
    "in matrix/vector notation?\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "$\\mathbf{v}^T \\cdot \\mathbf{A} \\cdot \\mathbf{w}$\n",
    "```\n",
    ":::\n",
    "\n",
    ":::{card} Exercise 3\n",
    "What is the type of the result of the following product?\n",
    "\n",
    "$\\mathit{v}_i \\cdot \\mathit{w}_j$\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "Second order tensor\n",
    "```\n",
    ":::\n",
    "\n",
    ":::{card} Exercise 4\n",
    "How would you write the product\n",
    "\n",
    "$\\mathit{A}_{ij} \\cdot \\mathit{v}_{i}$\n",
    "\n",
    "in matrix vector notation?\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "$\\mathbf{A}^T \\cdot \\mathbf{v}$\n",
    "```\n",
    ":::\n",
    "\n",
    ":::{card} Exercise 5\n",
    "How would you write the result of the product\n",
    "\n",
    "$\\mathit{v}_{i} \\cdot \\mathit{w}_{j}$\n",
    "\n",
    "in matrix vector notation?\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "$\\mathbf{v} \\cdot \\mathbf{w}^T$\n",
    "```\n",
    ":::\n",
    "\n",
    ":::{card} Exercise 6\n",
    "How would you write the product\n",
    "\n",
    "$\\mathbf{A} \\cdot \\mathbf{B}^T$\n",
    "\n",
    "in index notation?\n",
    "```{admonition} Solution\n",
    ":class: tip, dropdown\n",
    "$\\mathit{A}_{ik} \\cdot \\mathit{B}_{jk}$\n",
    "```\n",
    ":::"
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