Need help with questions 1 and 2

The following are some common (and important) properties and definitions about vectors: 1. Given two column vectors aRr1 and bRc1, the outer product is: ab=a0ar1b0bc1=a0bTar1bT=a0b0ar1b0a0bc1ar1bc1Rrc 2. Given two column vectors a and b both in Rr1, the inner product (or the dot product) is defined as: ab=aTb=[a0ar1]b0br1=i=0raibi where vT is the transpose of a vector, which converts between column and row vector alignment. The same idea extends to matrices as well. 3. Given a matrix MRrc, a matrix product is defined as: Mx=Mx0xc1=M0Mr1x=M0xMr1x 4. MRrc implies that the function f(x)=Mx can mapRc1Rr1. 5. M1Rdc and M2Rrd implies f(x)=M2M1x can map RcRr Questions (Vectors) Given the vector rules above and your own knowledge, try solving these: 1. Prove that (2)+(3) implies (4). In other words, use your understanding of the inner and matrix-vector products to explain why (4) has to be true. 2. Prove that (4) implies