The matrix P is the inverse of a matrix Q. If denotes the identity matrix, which one of the following options is correct?
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A square matrix B is skew-symmetric if
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Given that, {\text{A}} = \left[ {\begin{array}{*{20}{c}}
{ - 5}&{ - 3} \\
2&0
\end{array}} \right] and I = \left[ {\begin{array}{*{20}{c}}
1&0 \\
0&1
\end{array}} \right], the value A3 is
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Consider the matrices X(4 × 3), Y(4 × 3) and P(2 × 3). The order of [P(XTY)-1 PT]T will be
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The rank of the matrix \left[ {\begin{array}{*{20}{c}}
{ - 4}&1&{ - 1} \\
{ - 1}&{ - 1}&{ - 1} \\
7&{ - 3}&1
\end{array}} \right] is
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Consider the following linear system.
x + 2y - 3z = a
2x + 3y + 3z = b
5x + 9y - 6z = c
This system is consistent if a, b and c satisfy the equation
x + 2y - 3z = a
2x + 3y + 3z = b
5x + 9y - 6z = c
This system is consistent if a, b and c satisfy the equation
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Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a ≠ 0, b ≠ 0 with respective eigen vectors \left[ {\begin{array}{*{20}{c}}
{{{\text{x}}_1}} \\
{{{\text{x}}_2}} \\
{{{\text{x}}_3}}
\end{array}} \right],\left[ {\begin{array}{*{20}{c}}
{{{\text{y}}_1}} \\
{{{\text{y}}_2}} \\
{{{\text{y}}_3}}
\end{array}} \right]. If a ≠ b then x1y1 + x2y2 + x3y3 equals
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For which value of x will the matrix given below become singular?
\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\ 4&0&2 \\ {12}&6&0 \end{array}} \right]
\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\ 4&0&2 \\ {12}&6&0 \end{array}} \right]
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The number of solutions of the simultaneous algebraic equation y = 3x + 3 and y = 3x + 5 is:
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Given Matrix \left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}}
4&2&1&3 \\
6&3&4&7 \\
2&1&0&1
\end{array}} \right], the rank of the matrix is
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If {\text{A}} = \left[ {\begin{array}{*{20}{c}}
{2 + {\text{i}}}&3&{ - 1 + 3{\text{i}}} \\
{ - 5}&{\text{i}}&{4 - 2{\text{i}}}
\end{array}} \right], then AA∗ will be
(where, A∗ is the conjugate transpose of A)
(where, A∗ is the conjugate transpose of A)
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Consider the following system of linear equations:
3x + 2ky = -2
kx + 6y = 2
Here, x and y are the unknown and k is a real constant. The value of k for which there are infinite number of solutions is
3x + 2ky = -2
kx + 6y = 2
Here, x and y are the unknown and k is a real constant. The value of k for which there are infinite number of solutions is
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Consider the matrix as given below:
\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 0&4&7 \\ 0&0&3 \end{array}} \right]
Which one of the following options provides the CORRECT values of the eigen values of the matrix?
\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 0&4&7 \\ 0&0&3 \end{array}} \right]
Which one of the following options provides the CORRECT values of the eigen values of the matrix?
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The two Eigen values of the matrix \left[ {\begin{array}{*{20}{c}}
2&1 \\
1&{\text{p}}
\end{array}} \right] have a ratio of 3 : 1 for p = 2. What is another value of p for which the Eigen values have the same ratio of 3 : 1?
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The following simultaneous equations
x + y + z = 3
x + 2y + 3z = 4
x + 4y + kz = 6
will NOT have a unique solution for k equal to
x + y + z = 3
x + 2y + 3z = 4
x + 4y + kz = 6
will NOT have a unique solution for k equal to
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[A] is square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] - [A]T, respectively. Which of the following statements is TRUE?
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The Eigen values of the matrix \left[ {\text{P}} \right] = \left[ {\begin{array}{*{20}{c}}
4&5 \\
2&{ - 5}
\end{array}} \right] are
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If A is square symmetrical real valued matrix of dimensions 2n, then eigen values of A are
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The eigen values of the matrix given below are
\left[ {\begin{array}{*{20}{c}} 0&1&0 \\ 0&0&1 \\ 0&{ - 3}&{ - 4} \end{array}} \right]
\left[ {\begin{array}{*{20}{c}} 0&1&0 \\ 0&0&1 \\ 0&{ - 3}&{ - 4} \end{array}} \right]
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{\text{P}} = {\left[ {\begin{array}{*{20}{c}}
{ - 10} \\
{ - 1} \\
3
\end{array}} \right]^{\text{T}}},{\text{Q}} = {\left[ {\begin{array}{*{20}{c}}
{ - 2} \\
{ - 5} \\
9
\end{array}} \right]^{\text{T}}} and {\text{R}} = {\left[ {\begin{array}{*{20}{c}}
2 \\
{ - 7} \\
{12}
\end{array}} \right]^{\text{T}}} are three vectors. An orthogonal set of vectors having a span that contains P, Q, R is
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