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Determinantsmedium
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Three vectors in R3\mathbb{R}^3R3 form the rows of matrix AAA:\nv1=(200),v2=(030),v3=(115)\mathbf{v}_1 = \begin{pmatrix} 2 \\ 0 \\ 0 \end{pmatrix}, \quad \mathbf{v}_2 = \begin{pmatrix} 0 \\ 3 \\ 0 \end{pmatrix}, \quad \mathbf{v}_3 = \begin{pmatrix} 1 \\ 1 \\ 5 \end{pmatrix}v1​=​200​​,v2​=​030​​,v3​=​115​​\nThe volume of the parallelepiped spanned by these vectors equals ∣det⁡(A)∣|\det(A)|∣det(A)∣. What is this volume?