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

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

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

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 (λ - 1)x + (λ - 4)y + λ z = 5 λ x + (λ - 1)y + (λ - 4)z = 7 (λ + 1)x + (λ + 2)y - (λ + 2)z = 9 has infinitely…

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

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

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

Let α, β (α ≠ β) be the values of m, for which the equations x + y + z = 1, x + 2y + 4z = m, and x + 4y + 10z = m² have infinitely many…

If the system of linear equations 3x + y + β z = 3 2x + α y - z = -3 x + 2y + z = 4 has infinitely many solutions, then the value of 22β -…

If the system of equation 2x + λ y + 3z = 5 3x + 2y - z = 7 4x + 5y + μ z = 9 has infinitely many solutions, then λ² + μ² is equal to:

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

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

Let α be a solution of x² + x + 1 = 0, and for some a and b in ℝ, 4 a b 1 16 13 -1 -1 2 -2 -14 -8 = 0 0 0 If 4/α⁴ + m/α^a + n/α^b = 3, then…

Let A denote the matrix A = 2 0 1 1 1 0 1 0 1, and B = [B₁, B₂, B₃] where B₁, B₂, and B₃ are column matrices such that: AB₁ = 1 0 0, AB₂ =…

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(α, β) be a…

Consider the system of linear equations x + y + z = 4μ, x + 2y + 2λ z = 10μ, x + 3y + 4λ² z = μ² + 15, where λ, μ ∈ ℝ. Which one of the…

Consider the system of linear equations: x + y + z = 5, x + 2y + λ² z = 9, x + 3y + λ z = μ, where λ, μ ∈ ℝ. Then, which of the following…

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

If the system of equations x + (√2 sin α) y + (√2 cos α) z = 0, x + (\cos \alpha) y + (\sin \alpha) z = 0, x + (\sin \alpha) y − (\cos…

If the system of equations 11x + y + λ z = -5 2x + 3y + 5z = 3 8x - 19y - 39z = μ has infinitely many solutions, then λ⁴ - μ is equal to:

Consider the matrices A = 2 -5 3 m, B = 20 m, and X = x y. Let the set of all m, for which the system of equations AX = B has a negative…

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

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

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

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

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 α, β ∈ ℝ, suppose the system of linear equations x - y + z = 5 2x + 2y + α z = 8 3x - y + 4z = β has infinitely many solutions. Then α…

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

If a point P(α, β, γ) satisfying the equation α β γ 2 10 8 9 3 8 8 4 8 = 0 0 0 lies on the plane 2x + 4y + 3z = 5, then 6α + 9β + 7γ is…

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

For the system of linear equations α x + y + z = 1, x + α y + z = 1, x + y + α z = β, 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 + α z = 10 x + 3y + 5z = β which one of the following is NOT true:

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

Let S be the set of values of λ, for which the system of equations 6λ x - 3y + 3z = 4λ², 2x + 6λ y + 4z = 1, 3x + 2y + 3λ z = λ has no…

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

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 2x + y - z = 5 2x - 5y + λ z = μ x + 2y - 5z = 7 has infinitely many solutions, then (λ + μ)² + (λ - μ)² is…

Let the system of linear equations -x+2y-9z = 7 -x+3y+7z = 9 -2x+y+5z = 8 -3x+y+13z = λ have a unique solution x=α, y=β, z=γ. Then the…