How many solutions does the following system of linear equations have?
-x + 5y = -1; x - y = 2; x + 3y = 3
-x + 5y = -1; x - y = 2; x + 3y = 3
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Consider the following matrix.
{\text{A}} = \left[ {\begin{array}{*{20}{c}} 2&3 \\ {\text{x}}&{\text{y}} \end{array}} \right]
If the eigen values of A are 4 and 8, then
{\text{A}} = \left[ {\begin{array}{*{20}{c}} 2&3 \\ {\text{x}}&{\text{y}} \end{array}} \right]
If the eigen values of A are 4 and 8, then
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Let N be a 3 by 3 matrix with real number entries. The matrix N is such that N2 = 0. The eigen values of N are
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The eigen values of a (2 × 2) matrix X are -2 and -3. The eigen values of the matrix (X + ) (X + 5) are
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If the following system has non-trivial solution,
px + qy + rz = 0
qx + ry + pz = 0
rx + py + qz = 0
then which one of the following options is TRUE?
px + qy + rz = 0
qx + ry + pz = 0
rx + py + qz = 0
then which one of the following options is TRUE?
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The sum of the eigen values of the matrix given below is \left[ {\begin{array}{*{20}{c}}
1&2&3 \\
1&5&1 \\
3&1&1
\end{array}} \right].
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The following system of equations
x1 + x2 + 2x3 = 1
x1 + 2x3 + 3x3 = 2
x1 + 4x2 + ax3 = 4
has a unique solution. The only possible value(s) for a is/are
x1 + x2 + 2x3 = 1
x1 + 2x3 + 3x3 = 2
x1 + 4x2 + ax3 = 4
has a unique solution. The only possible value(s) for a is/are
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The eigen vector pair of the matrix \left[ {\begin{array}{*{20}{c}}
3&4 \\
4&{ - 3}
\end{array}} \right] is
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For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?
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The following vector is linearly dependent upon the solution to the previous problem
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The matrix {\text{A}} = \left[ {\begin{array}{*{20}{c}}
{\frac{3}{2}}&0&{\frac{1}{2}} \\
0&{ - 1}&0 \\
{\frac{1}{2}}&0&{\frac{3}{2}}
\end{array}} \right] has three distinct eigen values and one of its eigen vectors is \left[ {\begin{array}{*{20}{c}}
1 \\
0 \\
1
\end{array}} \right].
Which one of the following can be another eigen vector of A?
Which one of the following can be another eigen vector of A?
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The determinant \left| {\begin{array}{*{20}{c}}
{1 + {\text{b}}}&{\text{b}}&1 \\
{\text{b}}&{1 + {\text{b}}}&1 \\
2&{2{\text{b}}}&1
\end{array}} \right| equals to
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The solution of the system of equations x + y + z = 4, x - y + z = 0, 2x + y + z = 5 is
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Which one of the following is an eigen vector of the matrix \left[ {\begin{array}{*{20}{c}}
5&0&0&0 \\
0&5&5&0 \\
0&0&2&1 \\
0&0&3&1
\end{array}} \right]?
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The system of equation, given below, has
x + 2y + 4z = 2
4x + 3y + z = 5
3x + 2y + 3z = 1
x + 2y + 4z = 2
4x + 3y + z = 5
3x + 2y + 3z = 1
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The characteristic equation of a (3 × 3) matrix P is defined as
a(λ) = |P - λ| = λ3 + λ2 + 2λ + 1 = 0
If denotes identity matrix, then the inverse of matrix P will be
a(λ) = |P - λ| = λ3 + λ2 + 2λ + 1 = 0
If denotes identity matrix, then the inverse of matrix P will be
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For {\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&{\tan \,{\text{x}}} \\
{ - \tan {\text{ x}}}&1
\end{array}} \right], the determinant of ATA-1 is
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The value of the determinant \left| {\begin{array}{*{20}{c}}
1&3&2 \\
4&1&1 \\
2&1&3
\end{array}} \right| is
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The value of x3 obtained by solving following system of linear equation is
x1 + 2x2 - 2x3 = 4
2x1 + x2 + x3 = -2
-x1 + x2 - x3 = 2
x1 + 2x2 - 2x3 = 4
2x1 + x2 + x3 = -2
-x1 + x2 - x3 = 2
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Q100
Open questionFor what values of α and β, the following simultaneous equations have an infinite number of solutions?
x + y + z = 5
x + 3y + 3z = 9
x + 2y + αz = β
x + y + z = 5
x + 3y + 3z = 9
x + 2y + αz = β
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