" (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 adjoint of each of the following matrices: [[1, 2, 2],[ 2 ,1 ,2],[ 2, 2, 1]] (ii) [[1, 2, 5],[ 2, 3,1],[-1, 1, 1]] (iii) [[2,-1, 3],[ 4, 2, 5],[ 0, 4,-1]] (iv) [[2, 0,-1],[ 5, 1, 0],[ 1, 1, 3]] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

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)] .

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]]

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):}|

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, 0]][[-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]]

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ? (i) R={(4,1),(5,1),(6,7)} (ii) R={(2,3),(2,5),(3,3),(6,6)} (iii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (iv) R={(1,1),(2,1),(3,1),(4,1),(5,1)}

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):}|

In which octant the following points lie : (i) (2, 1, 4) (ii) (-1,2,4) (iii) (1,-3, 2) (iv) (1, 5,-6) (v) (2, -1, -3) (vi) (-2, 3, -5) (vii) (-4, -1, 3) (viii) (-1, -2, 3)

Find the slope of the line through the points (i) (1,2) , (4,2) (ii) (0,-4) , (-6,2) (iii) (4,-6) , (-2,-5) (iv) (4,6) , (2,12) (v) (3,-2) , (3,4)

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)|