List of top Mathematics Questions on System of Linear Equations asked in KEAM

The following system of equations \[ x + y + z = 1 \] \[ 2x + 3y - mz = 2 \] \[ 3x + 5y + 3z = 3 \] has no unique solution. Then the value of \( m \) is equal to

If $(x,y,z)$ is the solution of the equations $4x + y = 7$, $3y + 4z = 5$, $5x + 3z = 2$, then the value of $x + y + z$ equals

The values of \(k\) for which the system \[ (k+1)x + 8y = 0 \] \[ kx + (k+3)y = 0 \] has unique solution, are

If \( (x,y,z) \) is the solution of the equations \[ x - y - 2z = 3, 2x + y + 4z = 5, 4x - y - 2z = 11, \] then the value of \( y \) equals

If determinant of matrix is zero, then system is

If determinant of matrix is zero, then system is

If determinant of matrix is zero, then system is

The equations \( \lambda x - y = 2 \), \( 2x - 3y = -\lambda \), and \( 3x - 2y = -1 \) are consistent for:

If \( \begin{pmatrix} 2x+y & x+y \\ p-q & p+q \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix} \), then \( (x, y, p, q) \) equals:

If \( \begin{pmatrix} 1 & 2 & -3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \), then \( (x, y, z) \) is equal to:

The system of linear equations \( 3x + y - z = 2, x - z = 1 \) and \( 2x + 2y + az = 5 \) has unique solution when:

The number of solutions for the system of equations \( 2x + y = 4 \), \( 3x + 2y = 2 \), and \( x + y = -2 \) is:

The system of linear equations \( 3x + y - z = 2, x - z = 1 \) and \( 2x + 2y + az = 5 \) has unique solution when:

The number of solutions for the system of equations \( 2x + y = 4 \), \( 3x + 2y = 2 \), and \( x + y = -2 \) is:

The system of linear equations \( 3x + y - z = 2, x - z = 1 \) and \( 2x + 2y + az = 5 \) has unique solution when:

The number of solutions for the system of equations \( 2x + y = 4 \), \( 3x + 2y = 2 \), and \( x + y = -2 \) is: