Which of the following operations are defined and which are not defined? Explain

Question

Which of the following operations are defined and which are not defined? Explain briefly why or why not (it may help to preform these operations when possible).

i) A + 5I

ii) |Ab|

iii) (b^TA)^T

iv) b^T + b

v) b^Tb

vi) b*b^T

where T is the transposes of vector b or matrix A. I is the identity matrix


Please help!! Which of the following operations are defined and which are not defined? Explain briefly why or why not (it may help to preform these operations when possible).

i) A + 5I

ii) |Ab|

iii) (b^TA)^T

iv) b^T + b

v) b^Tb

vi) b*b^T

where T is the transposes of vector b or matrix A. I is the identity matrix


Please help!!

Explanation / Answer

(i) A+5I is possible if A and I are square matrices of same order i.e, assume A is of order n*n then I should be also n*n

(ii) |Ab| is possible if A has order m*n and b has order n*k i.e the no. of columns of first matrix should match with no. of rows of second matrix

(iii) Here also same as second question if the no. of columns of b^T should match with no. of rows of A

for (iv,v,vi) the matrix b should be a square matrix is n*n order or else its not possible.....

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