GATE PI
Engineering Mathematics
Linear Algebra
Previous Years Questions

## Marks 1

The eigen values of the matrix are $$\left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right]$$
The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is
The system of equations, given below, has $$x+2y+4z=2$$$$$4x+3y+z=5$$$ $$3x+2y+3z=1$$$For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } } \right]$$ are The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{ 1 & { - 1} & 0 \cr { - 1} & 2 & { - 1}... The value of the determinant$$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$is If$$A$$is square symmetric real valued matrix of dimension$$2n$$, then the eigen values of$$A$$are The determinant$$\left| {\matrix{ {1 + b} & b & 1 \cr b & {1 + b} & 1 \cr 1 & {2b} & 1 \cr } } \right|$$equ... The eigen values of the matrix$$M$$given are$$15, 3, $$and$$0.M = \left[ {\matrix{ 8 & { - 6} & 2 \cr { - 6} & 7 & ... If for a matrix, rank equals both the number of rows and number of columns, then the matrix is called The value of the following determinant $$\left[ {\matrix{ 1 & 4 & 9 \cr 4 & 9 & {16} \cr 9 & {16} & {25} \cr ... The matrix$$\left[ {\matrix{ 1 & { - 4} \cr 1 & { - 5} \cr } } \right]$$is an inverse of the matrix$$\left[ {\matrix{ 5 &... For the following matrix $$\left[ {\matrix{ 1 & { - 1} \cr 2 & 3 \cr } } \right]$$ the number of positive characteristic roots is Given matrix $$L = \left[ {\matrix{ 2 & 1 \cr 3 & 2 \cr 4 & 5 \cr } } \right]\,\,$$ and $$M = \left[ {\matrix{ 3 &... ## Marks 2$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$The system of algebraic equations given above has If a matrix$$A = \left[ {\matrix{ 2 & 4 \cr 1 & 3 \cr } } \right]$$and matrix$$B = \left[ {\matrix{ 4 & 6 \cr 5 &am... The value of $${x_3}$$ obtained by solving the following system of linear equations is $${x_1} + 2{x_2} - 2{x_3} = 4$$$ $$2{x_1} + {x_2} + {x_3} = ... The eigen vector pair of the matrix$$\left[ {\matrix{ 3 & 4 \cr 4 & { - 3} \cr } } \right]$$is The inverse of matrix$$\left[ {\matrix{ 0 & 1 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right] is
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