Home
Class 12
MATHS
If A =[[l(1),m(1),n(1)],[l(2),m(2),n(2)]...

If A =`[[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]]` then Find `A+I`

Text Solution

Verified by Experts

`Let A =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]`
`therefore A^(T) = [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]`
Now, `A A^(T) =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]xx [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]`
`= [[Sigmal_(1)^(2),Sigmal_(1) l_(2) ,Sigmal_(3)l_(1)],[Sigmal_(1)l_(2),Sigmal_(2)^(2), Sigmal_(2)l_(3) ],[Sigmal_(3)l_(1), Sigmal_(2)l_(3),Sigmal_(3)^(2)]]= [[1,0,0],[0,1,0],[0,0,1]]=I`
Hence, matrix A is orthogonal.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If l_(i)^(2)+m_(i)^(2)+n_(i)^(2)=1 , (i=1,2,3) and l_(i)l_(j)+m_(i)m_(j)+n_(i)n_(j)=0,(i ne j,i,j=1,2,3) and Delta=|{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}| then

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

If veca, vecb and vecc are any three non-coplanar vectors, then prove that points l_(1)veca+ m_(1)vecb+ n_(1)vecc, l_(2)veca+m_(2)vecb+n_(2)vecc, l_(3)veca+m_(3)vecb+ n_(3)vecc, l_(4)veca + m_(4)vecb+ n_(4)vecc are coplanar if |{:(l_(1),, l_(2),,l_(3),,l_(4)),(m_(1),,m_(2),,m_(3),,m_(4)), (n_1,,n_2,, n_3,,n_4),(1,,1,,1,,1):}|=0

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

If l_(n)=int_(0)^((pi)/(4)) tan^(n) xdx show that (1)/(l_(2)+l_(4)),(1)/(l_(3)+l_(5)),(1)/(l_(4)+l_(6)),(1)/(l_(5)+l_(7)),"...." from an AP. Find its common difference.

If l, l_(1), l_(2) and l _(3) be respectively the radii of the in-circle and the three escribed circles of a Delta ABC, then find l_(1)l_(2) l_(3)-l(l_(1)l_(2) +l_(2) l_(3)+l_(1) l_(3)).