4. Let V be the vector space of square n x n matrices over R. Let Tr: VR; A Tr(A) = a11 +a22+ +ann be the trace mapping on V. Here A = (aij). Show that Tr is a linear map.

Let M₂x2 be the vector space of all 2 x 2 matrices and define a linear transformation T: M2x2 → M2x2 by a [id] Describe the kernel of T. C T(A) = A + AT, where A = O No answer text provided. odlo 0 -a ° 0 O [1] :d is a real number} [9] : b is a real number} -b O (1 :d is a real number} (d c is a real number} °41 :d is a real number} : a,b,c,d are real numbers} [9] : b is a real number}

Please explain