3) If `[[x-3,2y-8],[z+2,6]]=[[5,2],[-2,a-4]]` then find `x,y,z` and `a`

If [[x-y, 2x+z],[2x-y,3z+omega]] =[[-1,5],[0,13]] find x+y+z+omega

If [(x,3x-y),(2x+z,3y-w)]=[(3,2),(4,7)], then find x+y+z+w.

If [(x-y ,z),(2x-y,omega)]=[(-1 ,4),( 0 ,5)] , find x ,\ y ,\ z ,\ omega .

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

If [x-y2x+z2x-y3z+w]=[-1 5 0 13] , find x ,\ y ,\ z ,\ wdot

If [(x,3x-y),(2x+z,3y-omega)]=[(3 ,2 ),(4 ,7)] , find x ,\ y ,\ z ,\ omega .

If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it to solve the following system of equation 5x - y + 4z = 5, 2x + 3y +5z = 2, 5x - 2y + 6z =-1

Find x,y,z from the following equation: [[x+y,2],[5+z,xy]]=[[6,2],[5,8]]

Using elementary transformations, find the inverse of the matrix A = [[ 8, 4, 3 ], [ 2, 1, 1 ], [ 1, 2, 2 ]] and use it to solve the following system of linear equations : 8x+4y+3z=19 2x+y+z=5 x+2y+2z=7

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)