Home
Class 12
MATHS
Evaluate the determinants (i) |(3,-1,-2...

Evaluate the determinants
(i) `|(3,-1,-2),( 0, 0,-1),( 3,-5, 0)|` (ii) `|(3,-4, 5), (1, 1,-2),( 2, 3, 1)|` (iii) `|(0, 1, 2),(-1, 0,-3),(-2, 3, 0)|` (iv) `|(2,-1,-2),( 0, 2,-1),( 3,-5, 0)|`

Text Solution

AI Generated Solution

Let's solve the determinants step by step. ### (i) Evaluate the determinant `|(3,-1,-2),(0,0,-1),(3,-5,0)|` 1. **Write the determinant**: \[ D_1 = \begin{vmatrix} 3 & -1 & -2 \\ ...
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.6|15 Videos
  • DETERMINANTS

    NCERT|Exercise SOLVED EXAMPLES|34 Videos
  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.5|18 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise QUESTION|3 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

Similar Questions

Explore conceptually related problems

Evalute the determinants : (i) |{:(3,-1,-2),(0,0,1),(3,-5,0):}| (ii) |{:(3,-4,5),(1,1,-2),(2,3,1):}| (iii) |{:(0,1,2),(-1,0,-3),(-2,3,0):}| (iv) |{:(2,-1,-2),(0,2,-1),(3,-5,0):}|

Find the equations of the plane passing through the following points : (i) A(2,1,0), B(3,-2,-2), C(3,1,7) (ii) A(1,1,1), B(1,-1,2), C(-2,-2,2) (iii) A(0,-1,0), B(2,1,-1), C(1,1,1) (iv) A(1,-2,5), B(0,-5,-1), C(-3,5,0) (v) (4,-1,-1), B(2,0,2),C(3,-1,2)

Find the inverse of the following matrices if exist : (i) |{:(5,-3),(2,2):}| (ii) |{:(1,-3),(-1,2):}| (iii) |{:(1,0,-1),(3,4,5),(0,-6,-7):}| (iv) |{:(1,-3,3),(2,2,-4),(2,0,2):}| (v) |{:(1,2,1),(1,-1,-2),(1,2,-1):}| (vi) |{:(4,-2,-1),(1,1,-1),(-1,2,4):}|

Compute the indicated products (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)]["2 3 4"] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)] .

Solve for x : |(2x,0,1),(0,1,2),(-1,2,0)| = |(1,0,0),(2,3,-4),(3,-3,5)|

Are the following matrices invertible ? |{:(2,-3),(1,4):}| (ii) |{:(7,0),(3,1):}| (iii) |{:(1,-2,-3),(1,-3,-4),(1,-4,-5):}| (iv) |{:(2,3,-1),(0,1,4),(-5,0,-2):}| (v) |{:(0,1,2),(1,2,3),(3,1,1):}|

Find the distance between the following pairs of points : (i) (-2, 1, -3) and (4, 3, -6) (ii) (9, -12, -8) and (0,0,0) (iii) (2,1,-3) and (2, 3, -3) (iv) (1,0,0) and (4, 4, 5)

Show that (i) [(5,-1),(6,7)][(2,1),(3,4)]!=[(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,1)][(-1,1,0),(0,-1,1),(2,3,4)]!=[(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)] .

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]