Determinants Matrices Question 99
Question: Consider the matrices $ A= \begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \\ \end{bmatrix} ,B=[ \begin{aligned} & \begin{matrix} 2 & 4 \\ \end{matrix} \\ & \begin{matrix} 0 & 1 \\ \end{matrix} \\ & \begin{matrix} -1 & 2 \\ \end{matrix} \\ \end{aligned} ],C= \begin{bmatrix} 3 \\ 1 \\ 2 \\ \end{bmatrix} $ Out of the given matrix products, which one is not defined.
Options:
A) $ {{(AB)}^{T}}C $
B) $ C^{T}C{{(AB)}^{T}} $
C) $ C^{T}AB $
D) $ A^{T}ABB^{T}C $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ A\to 3\times 3,B\to 3\times 2,C\to 3\times 1 $
$ AB\to 3\times 2\Rightarrow {{(AB)}^{T}}=2\times 3\Rightarrow {{(AB)}^{T}}C $ is defined
$ \Rightarrow C^{T}\to 1\times 3,\Rightarrow C^{T}C\to 1\times 1 $ Hence $ C^{T}C{{(AB)}^{T}} $ is not defined. Now, $ C^{T}AB $ is also defined. $ A^{T}\to 3\times 3,B^{T}\to 2\times 3;A^{T}A\to 3\times 3 $
$ BB^{T}\to 3\times 3\Rightarrow A^{T}ABB^{T}\to 3\times 3 $
$ \Rightarrow A^{T}ABB^{T}C $ is defined
BETA
