Solving Linear Equations (Matrix Method): JEE Questions & Solutions

If the system of equations 3x + y + 4z = 3 2x + y - z = -3 x + 2y + z = 4 has no solution, then the value of is equal to:

Let n be the number obtained on rolling a fair die. If the probability that the system cases x - ny + z = 6 x + (n-2)y + (n+1)z = 8 (n-1)y…

The system of linear equations x + y + z = 6 2x + 5y + az = 36 x + 2y + 3z = b has

If the system of linear equations: x + y + 2z = 6, 2x + 3y + az = a + 1, -x - 3y + bz = 2b, where a, b R, has infinitely many solutions,…

If the system of equations ( - 1)x + ( - 4)y + z = 5 x + ( - 1)y + ( - 4)z = 7 ( + 1)x + ( + 2)y - ( + 2)z = 9 has infinitely many…

The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + z =, has no solution if:

If the system of equations 2x - y + z = 4, 5x + y + 3z = 12, 100x - 47y + z = 212, has infinitely many solutions, then - 2 is equal to:

If the system of equations x + 2y - 3z = 2, 2x + y + 5z = 5, 14x + 3y + z = 33 has infinitely many solutions, then + is equal to:

Let, () be the values of m, for which the equations x + y + z = 1, x + 2y + 4z = m, and x + 4y + 10z = m^2 have infinitely many solutions.…

If the system of equations: aligned 3x + y + z &= 3 2x + y + z &= 2 x + 2y + z &= 4 aligned has infinitely many solutions, then the value…

If the system of equation 2x + y + 3z = 5 3x + 2y - z = 7 4x + 5y + z = 9 has infinitely many solutions, then ^2 + ^2 is equal to:

Let the system of equations be: 2x + 3y + 5z = 9, 7x + 3y - 2z = 8, 12x + 3y - (4 +)z = 16 -, which has infinitely many solutions. Then the…

Let the system of equations x + 5y - z = 1 4x + 3y - 3z = 7 24x + y + z = where, R, have infinitely many solutions. Then the number of the…

Let be a solution of x^2 + x + 1 = 0, and for some a and b in R, bmatrix 1 & 16 & 13 -1 & -1 & 2 -2 & -14 & -8 bmatrix bmatrix 4 a b…

Let A denote the matrix A = bmatrix 2 & 0 & 1 1 & 1 & 0 1 & 0 & 1 bmatrix, and B = [B1, B2, B3] where B1, B2, and B3 are column matrices…

Let for any three distinct consecutive terms a, b, c of an A.P., the lines ax + by + c = 0 be concurrent at the point P, and Q(,) be a…

Consider the system of linear equations x + y + z = 4, x + 2y + 2z = 10, x + 3y + 4 z = ^2 + 15. Which one of the following statements is…

Consider the system of linear equations: x + y + z = 5, x + 2y + 2z = 9, x + 3y + z =, where, R. Then, which of the following statements is…

If the system of linear equations: x - 2y + z = -4 2x + y + 3z = 5 3x - y + z = 3 has infinitely many solutions, then 12 + 13 is equal to:

If the system of equations x + ( 2) y + ( 2) z = 0, x + () y + () z = 0, x + () y − () z = 0 has a non-trivial solution, then in the…

If the system of equations 11x + y + z = -5 2x + 3y + 5z = 3 8x - 19y - 39z = has infinitely many solutions, then ^4 - is equal to:

Consider the matrices A = bmatrix 2 & -5 3 & m bmatrix, B = bmatrix 20 m bmatrix, and X = bmatrix x y bmatrix. Let the set of all m, for…

For, R, if the system of equations: 3x + 5y + z = 3 7x + 11y - 9z = 2 97x + 155y - 189z = has infinitely many solutions, then + 2 equals:

Consider the matrices A = bmatrix 2 & -5 3 & m bmatrix, B = bmatrix 20 m bmatrix, and X = bmatrix x y bmatrix. Let the set of all m, for…

If the system of equations x + 2y + 3z = 3 (i) 4x + 3y - 4z = 4 (ii) 8x + 4y - z = 9 + (iii) has infinitely many solutions, then the…

Let S1 and S2 be respectively the sets of all a R - 0 for which the system of linear equations: aligned ax + 2ay - 3az &= 1, (2a + 1)x +…

Consider the following system of equations: - x + 2y + z = 1 - 2 x + 3y + z = 1 - 3x + y + 2z = For some, R. Then which of the following is…

Let the system of linear equations x + y + kz = 2 2x + 3y - z = 1 3x + 4y + 2z = k have infinitely many solutions. Then the system (k+1)x +…

For, R, suppose the system of linear equations x - y + z = 5 2x + 2y + z = 8 3x - y + 4z =

For the system of linear equations: x + y + z = 6 x + y + 7z = 3 x + 2y + 3z = 14 Which of the following is NOT true?

If a point P(,,) satisfying the equation pmatrix 2 & 10 & 8 9 & 3 & 8 8 & 4 & 8 pmatrix pmatrix pmatrix = pmatrix 0 0 0 pmatrix lies on the…

Let S denote the set of all real values of such that the system of equations x + y + z = 1 x + y + z = 1 x + y + z = 1 is inconsistent.…

For the system of linear equations x + y + z = 1, x + y + z = 1, x + y + z =, which one of the following statements is NOT correct?

If the system of equations x+y+az = b, 2x + 5y + 2z = 6, x+2y+3z = 3 has infinitely many solutions, then 2a+3b is equal to:

For the system of equations x + y + z = 6 x + 2y + z = 10 x + 3y + 5z = which one of the following is NOT true:

For the system of linear equations 2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y + z =, which of the following is NOT correct?

Let S be the set of values of, for which the system of equations aligned 6 x - 3y + 3z &= 4 ^2, 2x + 6 y + 4z &= 1, 3x + 2y + 3 z &=…

If the system of linear equations: 7x + 11y + z = 13, 5x + 4y + 7z =, 175x + 194y + 57z = 361 has infinitely many solutions, then + + 2 is…

For the system of linear equations 2x + 4y + 2az = b, x + 2y + 3z = 4, 2x - 5y + 2z = 8, which of the following is NOT correct?

If the system of equations aligned 2x + y &= -5 2x - 5y + z &= -9 x + 2y - 5z &= 7 aligned has infinitely many solutions, then (x + y)^2 +…

Let the system of linear equations aligned -x+2y-9z &= 7 -x+3y+7z &= 9 -2x+y+5z &= 8 -3x+y+13z &= aligned have a unique solution x=, y=,…