If is an eigen vector of the following matrix \left[ {\begin{array}{*{20}{c}}
1&{ - 1}&0 \\
{ - 1}&2&{ - 1} \\
0&{ - 1}&1
\end{array}} \right] then corresponding eigen value is
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The eigen values of the following matrix are \left[ {\begin{array}{*{20}{c}}
{ - 1}&3&5 \\
{ - 3}&{ - 1}&6 \\
0&0&3
\end{array}} \right]
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Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = -1. Then the eigen values of the matrix A19 are
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How many of the following matrices have an eigen value 1?
\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&1 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1&{ - 1} \\ 1&1 \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 1&{ - 1} \end{array}} \right]
\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&1 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1&{ - 1} \\ 1&1 \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 1&{ - 1} \end{array}} \right]
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A real square matrix A is called skew-symmetric if
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If {\text{R}} = \left[ {\begin{array}{*{20}{c}}
1&0&{ - 1} \\
2&1&{ - 1} \\
2&3&2
\end{array}} \right], then top row of R-1 is
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Let, {\text{A}} = \left[ {\begin{array}{*{20}{c}}
2&{ - 0.1} \\
0&3
\end{array}} \right] and {{\text{A}}^{ - 1}} = \left[ {\begin{array}{*{20}{c}}
{\frac{1}{2}}&{\text{a}} \\
0&{\text{b}}
\end{array}} \right].
Then (a + b) = ?
Then (a + b) = ?
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We have a set of 3 linear equations in 3 unknowns. 'X Y' means X and Y are equivalent statements and 'X Y' means X and Y are not equivalent statements.
P : There is a unique solution.
Q : The equations are linearly independent.
R : All eigen values of the coefficient matrix are nonzero.
S : The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
P : There is a unique solution.
Q : The equations are linearly independent.
R : All eigen values of the coefficient matrix are nonzero.
S : The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
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The elgen values of the matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&{ - 1}&5 \\
0&5&6 \\
0&{ - 6}&5
\end{array}} \right] are
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Consider the following simultaneous equations (with c1 and c2 being constants):
3x1 + 2x2 = c1
4x1 + x2 = c2
The characteristics equation for these simultaneous equations is
3x1 + 2x2 = c1
4x1 + x2 = c2
The characteristics equation for these simultaneous equations is
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For the matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
3&{ - 2}&2 \\
0&{ - 2}&1 \\
0&0&1
\end{array}} \right], one of the eigen values is equal to -2. Which of the following is an eigen vector?
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What are the eigen values of the following 2 × 2 matrix?
\left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ { - 4}&5 \end{array}} \right]
\left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ { - 4}&5 \end{array}} \right]
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Eigen values of the matrix \left[ {\begin{array}{*{20}{c}}
3&{ - 1}&{ - 1} \\
{ - 1}&3&{ - 1} \\
{ - 1}&{ - 1}&3
\end{array}} \right] are
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If {\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&5 \\
6&2
\end{array}} \right] and {\text{B}} = \left[ {\begin{array}{*{20}{c}}
3&7 \\
8&4
\end{array}} \right],\,{\text{A}}{{\text{B}}^{\text{T}}} is equal to
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The number of linearly independent eigen vectors of \left[ {\begin{array}{*{20}{c}}
2&1 \\
0&2
\end{array}} \right] is
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A 3 × 3 matrix P is such that, P3 = P. Then the eigen values of P are
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One of the eigen vectors of matrix is \left[ {\begin{array}{*{20}{c}}
{ - 5}&2 \\
{ - 9}&6
\end{array}} \right] is
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For the matrix \left[ {\begin{array}{*{20}{c}}
4&2 \\
2&4
\end{array}} \right] the eigen value corresponding to the eigen vector \left[ {\begin{array}{*{20}{c}}
{101} \\
{101}
\end{array}} \right] is
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The eigen values of matrix \left[ {\begin{array}{*{20}{c}}
9&5 \\
5&8
\end{array}} \right] are
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Consider the 5 × 5 matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&2&3&4&5 \\
5&1&2&3&4 \\
4&5&1&2&3 \\
3&4&5&1&2 \\
2&3&4&5&1
\end{array}} \right]
It is given that A has only one real eigen value.
Then the real eigen value of A is
It is given that A has only one real eigen value.
Then the real eigen value of A is
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