Question: of a partitioned matrix). Let a be the column vector (1 2 ... In] 5 2 (a) For A = -1 0 3 and a

of a partitioned matrix). Let a be the column vector (1 2 ... In] 5 2 (a) For A = -1 0 3 and a = CO D N , verify that 2 4 0 ( * ) Ad = X1Al + 2A2 + ... + In An (b) Show that in general the product of a matrix and a vector can be expressed as a linear combination of the column vectors of the matrix, that is, show that (*) is a true statement independent of the particular matrices in part (a). Do this all a12 a13 by showing this true for A = a21 a22 a 23 and * = 2 2 a31 a32 a33 Can square matrices larger that 3 x 3 be taken apart in this way

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