Compute the product using (a) the definition where Ax is the linear combination

Question

Compute the product using (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights, and (b) the row-vector rule for computing Ax. If a product is undefined, explain why. (a) Compute the product using the definition where Al is the linear combination of the columns of A using the corresponding entries in x as weights. If the product is undefined, explain why. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. Ax = B. The matrix-vector Ax is not defined because the number of columns in matrix A does not match the number of entries in the vector x. C)C. The matrix-vector Ax is not defined because the number of rows in matrix A does not match the number of entries in the vector x.

Explanation / Answer

for a matrix multiplication to exist then number of coloums in first matrix must be equal to rows in second matrix

ILLUSTRATION:

let P= ( a x b) order , Q=( c x d)   

the P x Q exists if and only if b=c and we get resultant matrix order as ( a x b)

if ( b not= c) then matrix multiplication does not exist

in given problem ,P = ( 3 x 2) ,Q = ( 3 x 1 ) so matrix multiplication doesnot exist

ANS: option (C)

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