Without expanding, show that the value of each of the following determinants is zero: `|49 1 6 39 7 4 26 2 3|` (ii) `|0x y-x0z-y-z0|` (iii) `|1 43 6 7 35 4 3 17 2|`

Without expanding, show that the value of the following determinant is zero: |[49, 1, 6], [39, 7, 4], [26, 2, 3]|

Without expanding,show that the values of the following determinants are zero: |(1,4,y+z),(1,4,z+x),(1,4,x+y)|

Without expanding,show that the values of the following determinants are zero: |(x,y,z),(x+3a,y+3b,z+3c),(a,b,c)|

Find the values of x, y and z from the following equations: (i) [4 3x5]=[y z1 5] (ii) [x+y3 5+z x y]=[6 2 5 8] (iii) [x+y+z x+z y+z]=[9 5 7]

Show that each of the following pairs of planes are at right angles: i) 3x+4y-5z=7 and 2x+6y+6z+7=0 ii) x-2y+4z=10 and 18x+17y+4z=49

Find the values of x and y from each of the following matrix equation : (i) [{:(x+y),(x-y):}]=[(3)/(1)](ii) [{:(x+y,7),(0,2x):}]=[{:(-1,7),(0,6):}]

Find the values of x and y from each of the following matrix equation : (i) [{:(x+y),(x-y):}]=[(3)/(1)](ii) [{:(x+y,7),(0,2x):}]=[{:(-1,7),(0,6):}]

In the following determine whether the given planes are parallel or perpendicular and in case they are neither, find the angles between them : (i) 7x + 5y + 6z + 30 = 0 and 3x - y - 10z + 4 = 0 (ii) 2x + y + 3z - 2 = 0 and x - 2y + 5 = 0 (iii) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z - 1 = 0 (iv) 2x - y + 3z - 1 = 0 and 2x - y + 3z + 3 = 0 (v) 4x + 8y + z - 8 = 0 and y + z - 4 = 0.

"Find the values of x,y,z and a satisfying the following matrix "[(x+3,2y+x),(z-1,4a-6)]"="[(0,-7),(3,1)]"