Q161
Open questionX = [x1, x2, ... xn]T is an n-tuple nonzero vector. The n × n matrix V = XXT
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Q162
Open questionWhich one of the following statements is NOT true for a square matrix A?
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Q163
Open questionFor any real, square and non-singular matrix B, the detB-1 is
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Q164
Open questionGiven a system of equations:
x + 2y + 2z = b1
5x + y + 3z = b2
Which of the following is true regarding its solution?
x + 2y + 2z = b1
5x + y + 3z = b2
Which of the following is true regarding its solution?
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Q165
Open questionThe matrix \left( {\begin{array}{*{20}{c}}
2&{ - 4} \\
4&{ - 2}
\end{array}} \right) has
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Q166
Open questionThe inverse of the matrix \left[ {\begin{array}{*{20}{c}}
2&3&4 \\
4&3&1 \\
1&2&4
\end{array}} \right] is
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Q167
Open questionThe condition for which the eigen values of the matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
2&1 \\
1&{\text{k}}
\end{array}} \right] are positive, is
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Q168
Open questionGiven that the determinant of the matrix \left[ {\begin{array}{*{20}{c}}
1&3&0 \\
2&6&4 \\
{ - 1}&0&2
\end{array}} \right] is -12, the determinant of the matrix \left[ {\begin{array}{*{20}{c}}
2&6&0 \\
4&{12}&8 \\
{ - 2}&0&4
\end{array}} \right] is
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Q169
Open questionFor the matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
5&3 \\
1&3
\end{array}} \right], ONE of the normalized eigen vectors is given as
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Q170
Open questionThe product of eigen values of the matrix P is {\text{P}} = \left[ {\begin{array}{*{20}{c}}
2&0&1 \\
4&{ - 3}&3 \\
0&2&{ - 1}
\end{array}} \right]
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Q171
Open questionConsider a non-homogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be
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Q172
Open questionThe dimension of the null space of the matrix \left[ {\begin{array}{*{20}{c}}
0&1&1 \\
1&{ - 1}&0 \\
{ - 1}&0&1
\end{array}} \right] is
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Q173
Open questionX and Y are non-zero square matrices of size n × n. If XY = 0n × n then
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Q174
Open questionA is m × n full rank matrix with m > n and is an identity matrix. Let matrix A' = (ATA)-1AT, Then, which one of the following statement is TRUE?
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Q175
Open questionThe minimum and the maximum eigen values of the matrix \left[ {\begin{array}{*{20}{c}}
1&1&3 \\
1&5&1 \\
3&1&1
\end{array}} \right] are -2 and 6, respectively. What is the other eigen value?
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Q176
Open questionConsider the matrix \left[ {\begin{array}{*{20}{c}}
5&{ - 1} \\
4&1
\end{array}} \right] . Which one of the following statements is TRUE for the eigen values and eigen vectors of this matrix?
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Q177
Open questionLet M be a real 4 × 4 matrix. Consider the following statements:
S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?
S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?
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Q178
Open questionThe smallest and largest Eigen values of the following matrix are \left[ {\begin{array}{*{20}{c}}
3&{ - 2}&2 \\
4&{ - 4}&6 \\
2&{ - 3}&5
\end{array}} \right]
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Q179
Open questionEigen values of a matrix {\text{S}} = \left[ {\begin{array}{*{20}{c}}
3&2 \\
2&3
\end{array}} \right] are 5 and 1. What are the eigen values of the matrix S2 = SS?
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Q180
Open questionIf any two columns of a determinant {\text{P}} = \left| {\begin{array}{*{20}{c}}
4&7&8 \\
3&1&5 \\
9&6&2
\end{array}} \right| are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?
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