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- Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrixFind the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.In Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|In Exercises 1-12, determine whether T is a linear transformation. 4. defined by , where B is a fixed matrix