SATHEE: Matrices and Determinants 4 Question 3

Matrices and Determinants 4 Question 3

3. If the system of linear equations

$x + y + z = 5$

$x + 2 y + 2 z = 6$

$x + 3 y + λ z = μ, (λ, μ \in R),$ has infinitely many solutions, then the value of $λ + μ$ is

(2019 Main, 10 April I)

(a) 7

(b) 12

(d) 9

Show Answer

Answer:

Correct Answer: 3. (c)

Solution:

Given system of linear equations

$\begin{matrix} x + y + z = 5 \\ x + 2 y + 2 z = 6 \\ x + 3 y + λ z = μ \end{matrix}$

$(λ, μ \in R)$

The above given system has infinitely many solutions, then the plane represented by these equations intersect each other at a line, means $(x + 3 y + λ z - μ)$

$= p (x + y + z - 5) + q (x + 2 y + 2 z - 6)$

$= (p + q) x + (p + 2 q) y + (p + 2 q) z - (5 p + 6 q)$

On comparing, we get

$\begin{array}{lc} p + q = 1, p + 2 q = 3, p + 2 q = λ \\ and & 5 p + 6 q = μ \\ So, & (p, q) = (- 1, 2) \\ \Rightarrow & λ = 3 and μ = 7 \\ \Rightarrow & λ + μ = 3 + 7 = 10 \end{array}$

Matrices and Determinants 4 Question 3

3. If the system of linear equations

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Matrices and Determinants 4 Question 3

3. If the system of linear equations

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu