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Matrices and Determinants question

2022 · Shift 2 · Q24

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JEE Advanced
Mathematics
Matrices and Determinants
2022 · Shift 2 · Q24

Matrices and Determinants question

2022 · Shift 2 · Q24

JEE AdvancedMathematicsMatrices and DeterminantsNumerical+3 / −1

Let

\beta

be a real number. Consider the matrix

A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right)

If

A^{7}-(\beta-1) A^{6}-\beta A^{5}

is a singular matrix, then the value of

9 \beta

is

\underline{\hspace{2cm}}

.

Numerical answer

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