Fun with Matrices!

Algebra Level 3

If the matrix

D= [ e x s i n x c o s x l n ( 1 + x ) ] \begin{bmatrix} { e }^{ x } & sinx \\ cosx\quad \quad & ln(1+x) \end{bmatrix}\quad

and,

Det(D)= A + B x + C x 2 + . . . . . \quad A+B{ x }+C{ x }^{ 2 }+.....

Find the value of A +B


The answer is 0.

Emil Joseph by Emil Joseph , 23, India

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1 solution

Akshat Sharda
May 27, 2017

Putting x = 0 x=0 gives A = 0 A=0 and putting x = 0 x=0 after differentiating D D gives B = 0 B=0 .

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