Find the values of x,y,z and r from the equation `2[{:(x,z),(y,r):}]+3[{:(1,-1),(0,2):}]=3[{:(3,5),(4,6):}]`

Find the value of x and y from the equation. [{:(3x+7,5),(y+1,2-3x):}]=[{:(-2,5),(1,11):}]

Solve the equation for x,y,z and t,if 2[{:(x,z),(y,t):}]+3[{:(1,-1),(0,2):}]=3[{:(3,5),(4,6):}] .

Find the values of x, y and z from the following equations : (i) [{:(4,3),(x,5):}]=[{:(y,z),(1,5):}] (ii) [{:(x+y,2),(5+z,xy):}]=[{:(6,2),(5,8):}] (iii) [{:(x+y+z),(x+z),(y+z):}]=[{:(9),(5),(7):}]

Find the values of x,y,z if the matrix A=[{:(0,2y,z),(x,y,-z),(x,-y,z):}] satisfy the equation A'A=I.

Find the distance of the point (3,-2,1) from the plane 2x-y+2z + 3 = 0.

Find the distance of a point (2, 4, -1) from the line (x+5)/(1)=(y+3)/(4)=(z-6)/(-9) .

Given 3[{:(x,y),(z,w):}]=[{:(x,6),(-1,2w):}]+[{:(4,x+y),(z+w,3):}] , find the values of x,y,z and w.

Find the nature of solution for the given system of equation: x+2y+3z=1;2x+3y+4z=3;3x+4y+5z=0