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|`

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)|

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):}|

Evaluate the following: ([1 3-1-4]+[3-2-1 1])[1 3 5 2 4 6] (ii) [1 2 3][1 0 2 2 0 1 0 1 2][2 4 6] (iii) [1-1 0 2 2 3]([1 0 2 2 0 1]-[0 1 2 1 0 2])

Write Minors and Cofactors of the elements of following determinants: (i) |1 0 0 0 1 0 0 0 1| (ii) |1 0 4 3 5-1 0 1 2|

Show that A B!=B A in each of the following cases: A=[5-1 6 7] and B=[2 1 3 4] (ii) A=[-1 1 0 0-1 1 2 3 4] and B=[1 2 3 0 1 0 1 1 0] (iii) A=[1 3 0 1 1 0 4 1 0] and B=[0 1 0 1 0 0 0 5 1]

Find the value of. (i) (3^@+4^(-1)) xx 2^2 (ii) (2^(-1)xx 4^(-1))-: 2^(-1) (iii) (1/2)^-2 + (1/3)^-2 + (1/4)^-2 (iv) (3^-1 + 4^-1+ 5^(-1))^0 (v) {((-2)/3)^-2}^2

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)

" (i) |[2,5], [6,0]| (ii) |[2,-1],[3,2]| (iii) |[0,4],[5,-1]| (iv) |[(1)/(2),1],[(3)/(4),(1)/(5)]|

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) [[2, 3 ,4 ],[3, 4 ,5],[ 4, 5, 6]][[1,-3, 5],[ 0, 2, 4],[ 3, 0, 5]] (v) [[2,1],[3,2],[-1,1]] [[1, 0, 1],[-1, 2 ,1]] (vi) [[3,-1, 3],[1,0,2]] [[2 ,-3],[ 1, 0],[ 3, 1]]