4. Verify all vector space axioms and determine, if the set of all triples of real numbers (x, y, z) is a vector space under the given operations ( x, y, z) + ( x , y , z ) = (x + x ,yty ,z+z) and k(x, y, z) = (kx, y, z)Date ................mmm We need to show that ( K + m ) ( x , 4 / 2 ) = k ( x , y, z ) + m ( x , 4 , 2 ) Solving L.H.S Firstly = > ( k + m ) ( x , y , z ) = ( k + m j > > y / z ) Now solving R.H'S k l x , y , z ) + m ( x , u , z ) . = ( kx , y , z ) + (mx , 4 , z ) $ 5 = ( x tmix , y + y , z + z so we can see clearly ( K + m ) x , y + y , z + z z ( ( + m j x , y , z ) So ( K + m ) ( x , 4 / z ) 7 ( k + m j x , y , z ) Hence 8 property satisfied, so the given set of triples of Real No is not a vector space