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3 and 4 .Determinants and Matrices
normal
Consider the matrices $A =$ $\left[ {\begin{array}{*{20}{c}}4&6&{ - 1}\\3&0&2\\1&{ - 2}&5\end{array}} \right]$ , $B =$ $\left[ {\begin{array}{*{20}{c}}2&4\\0&1\\{ - 1}&2\end{array}} \right]$ , $C =$ $\left[{\begin{array}{*{20}{c}}3\\1\\2\end{array}} \right]$ . Out of the given matrix products
$(i)$ $(AB)^TC$ $(ii)$ $C^TC(AB)^T$ $(iii)$ $C^TAB$ and $(iv)$ $A^TABB^TC$
A
exactly one is defined
B
exactly two are defined
C
exactly three are defined
D
all four are defined
Solution
$(i), (iii)$ and $(iv)$ are correct
Standard 12
Mathematics
