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Engineering Maths · all questions

Linear Algebra
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The eigen values of the matrix \left[ {\begin{array}{*{20}{c}} 4&{ - 2} \\ { - 2}&1 \end{array}} \right]

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For the set of equations
x1 + 2x2 + x3 + 4x4 = 2
3x1 + 6x2 + 3x3 + 12x4 = 6
the following statement is true:

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Let A be an m × n matrix and Ban n × m matrix. It is given that determinant (m + AB) = determinant (n + BA), where k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right]

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