﻿ For what real values of k, the system of equations x + 2y + z = 1; x + 3y + 4z = k; x + 5y + 10z = k2 has solution? Find the solution of each case. : Kaysons Education

# For What Real Values Of K, The System Of Equations x + 2y + Z = 1; X + 3y + 4z = K; X + 5y + 10z = K2 has Solution? Find The Solution Of Each Case.

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## Question

### Solution

Correct option is

∴  Solution is not unique

The system will have infinite solution if

Δ1 = 0, Δ2 = 0, Δ3 = 0

Δ1 = 0 ⇒ k2 – 3k + 2 = 0  ∴  k = 1, 2

For these values Δ2 and Δ3 are also zero.

Now take

#### SIMILAR QUESTIONS

Q1

The values of λ for which the system of equations

(λ + 5)x + (λ – 4)y + z = 0

(λ – 2)x + (λ + 3)y + z = 0

λx + λy + z = 0

has a non – trivial solution is (are)

Q2

Number of real values of λ for which the system of equations

(λ + 3)x + (λ + 2)y + z = 0

3x + (λ + 3)y + z = 0

2x + 3y + z = 0

has a non – trivial solution is

Q3

The values of λ for which the system of equations

2x + y + 2z = 2,

x – 2y + z = – 4

x + y + λz = 4

has no solution is

Q4

Evaluate the determinant without expansion as for as possible.

Q5
Q7

Then f (100) is equal to

Q8
Q9

The number of values of k for which the system of equations

(k + 1) x + 8y = 4k

kx + (k + 3) y = 3k – 1

has infinitely many solution is

Q10

Let aij denoted the element of the ith row and jth column in 3 × 3 determinant (1 ≤ i ≤ 3, 1 ≤ j ≤ 3) and let aij – aij for every I and j. then the determinant has all the principle diagonal elements as