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MATH / For a matrix M, the trace of M is defined as the sum of its diagonal elements. For example, operatorname{Tr} begin{pmatrix} a & b c & d end{pmatrix} = a + d.Given Tr(A)=2 and …

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problem

For a matrix M,\mathbf{M}, the trace of M\mathbf{M} is defined as the sum of its diagonal elements. For example, \[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given Tr(A)=2\operatorname{Tr} (\mathbf{A}) = 2 and Tr(A2)=30,\operatorname{Tr} (\mathbf{A}^2) = 30, find detA.\det \mathbf{A}.
Plain-text mathematical notation (without MathML)
For a matrix M, the trace of M is defined as the sum of its diagonal elements.  For example,
\[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given Tr(A)=2 and Tr(A²)=30, find detA.
Original LaTeX notation
For a matrix $\mathbf{M},$ the trace of $\mathbf{M}$ is defined as the sum of its diagonal elements.  For example,
\[\operatorname{Tr} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = a + d.\]Given $\operatorname{Tr} (\mathbf{A}) = 2$ and $\operatorname{Tr} (\mathbf{A}^2) = 30,$ find $\det \mathbf{A}.$

level

Level 4

type

Precalculus

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Source and history

task_id
15bf4cf1-4a79-501a-99e5-2b8aadc9844e
task_key
precalculus--test--15bf4cf1-4a79-501a-99e5-2b8aadc9844e
task_revision_id
1
config / split
precalculus / test

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