- #1

AGNuke

Gold Member

- 455

- 9

**If the system of Linear Equations**

[tex]x+y+z=6[/tex]

[tex]x+2y+3z=14[/tex]

[tex]2x+5y+\lambda z=\mu[/tex]

**has infinite number of solution in x, y, z**

I need to find out two things

**1. The value of λ**

**2. Maximum value of**[tex](\mu x+\lambda y-20z)sin^2\theta+(\lambda x+\mu y+64z)cos2\theta, \theta \in \mathbb{R}[/tex]

**is 272**

I used the Matrix method of AX=B to find out λ by solving for A=0; I got the answer 8, and it is correct.

Now my catch is to validate the second question. It is given true, I just need to validate. I tried to solve it with the three existing equations but I was unable to get answer.

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