The rank of the matrix {\text{M}} = \left[ {\begin{array}{*{20}{c}}
5&{10}&{10} \\
1&0&2 \\
3&6&6
\end{array}} \right] is
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Linear Algebra
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One of the eigen vectors of the matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
2&2 \\
1&3
\end{array}} \right] is
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The lowest Eigen value of the 2 × 2 matrix \left[ {\begin{array}{*{20}{c}}
4&2 \\
1&3
\end{array}} \right]
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Which one of the following statements is TRUE about every n × n matrix with only real eigen values?
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The equation \left[ {\begin{array}{*{20}{c}}
2&{ - 2} \\
1&{ - 1}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{{{\text{x}}_1}} \\
{{{\text{x}}_2}}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
0 \\
0
\end{array}} \right] has
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Consider the system of simultaneous equations
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has
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The system of equations
x + y + z = 6
x + 4y + 6z = 20
x + 4y + z =
has NO solution for values of and given by
x + y + z = 6
x + 4y + 6z = 20
x + 4y + z =
has NO solution for values of and given by
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Let the eigen values of a 2 × 2 matrix A be 1, -2 with eigen vectors x1 and x2 respectively. Then the eigen values and eigen vectors of the matrix A2 - 3A + 4 would, respectively, be
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The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is
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If the entries in each column of a square matrix M add up to 1, then an eiqen value of M is
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The sum of Eigen values of matrix, [M] is where \left[ {\text{M}} \right] = \left[ {\begin{array}{*{20}{c}}
{215}&{650}&{795} \\
{655}&{150}&{835} \\
{485}&{355}&{550}
\end{array}} \right]
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The set of equations
x + y + z = 1
ax - ay + 3z = 5
5x - 3y + az = 6
has infinite solution if a = ?
x + y + z = 1
ax - ay + 3z = 5
5x - 3y + az = 6
has infinite solution if a = ?
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Consider the system of equations A(n × n) X(n × 1) = λ(n × 1) where, λ is a scalar. Let (λi, xi) be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let be a
(n × n) unit matrix. Which one of the following statement is NOT correct?
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The value of x for which all the eigen-values of the matrix given below are real is \left[ {\begin{array}{*{20}{c}}
{10}&{5 + {\text{j}}}&4 \\
{\text{x}}&{20}&2 \\
4&2&{ - 10}
\end{array}} \right]
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The system of linear equations \left[ {\begin{array}{*{20}{c}}
2&1&3 \\
3&0&1 \\
1&2&5
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{\text{a}} \\
{\text{b}} \\
{\text{c}}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
5 \\
{ - 4} \\
{14}
\end{array}} \right] has
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The matrix {\text{P}} = \left[ {\begin{array}{*{20}{c}}
0&0&1 \\
1&0&0 \\
0&1&0
\end{array}} \right] rotates a vector about the axis \left[ {\begin{array}{*{20}{c}}
1 \\
1 \\
1
\end{array}} \right] by angle of
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If a square matrix of order 100 has exactly 15 distinct eigen values, the degree of the minimal polynomial is
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A matrix has eigen values -1 and -2. The corresponding eigen vectors are \left[ {\begin{array}{*{20}{c}}
1 \\
{ - 1}
\end{array}} \right] and \left[ {\begin{array}{*{20}{c}}
1 \\
{ - 2}
\end{array}} \right] respectively. The matrix is
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Let A, B, C, D be n × n matrices, each with nonzero determinant, If ABCD = , then B-1 is
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The eigen vectors of the matrix \left[ {\begin{array}{*{20}{c}}
1&2 \\
0&2
\end{array}} \right] are written in the form \left[ {\begin{array}{*{20}{c}}
1 \\
{\text{a}}
\end{array}} \right] and \left[ {\begin{array}{*{20}{c}}
1 \\
{\text{b}}
\end{array}} \right]. What is a + b = ?
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