Product Of Matrices

To find $(PQ)'$ , we first compute the product $PQ$ where:

$P$ is a column matrix of order $3%20%5Ctimes%201$
$Q$ is a row matrix of order $1%20%5Ctimes%203$

The product $PQ$ will be a $3%20%5Ctimes%203$ matrix given by:

$PQ%20%3D%20%5Cbegin%7Bbmatrix%7D-1%20%5C%5C2%20%5C%5C1%5Cend%7Bbmatrix%7D%5Ctimes%5Cbegin%7Bbmatrix%7D2%20%26%20-4%20%26%201%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D-2%20%26%204%20%26%20-1%20%5C%5C4%20%26%20-8%20%26%202%20%5C%5C2%20%26%20-4%20%26%201%5Cend%7Bbmatrix%7D$

Next, we find the transpose $(PQ)'$ :

$(PQ)'%20%3D%20%5Cbegin%7Bbmatrix%7D-2%20%26%204%20%26%20-1%20%5C%5C4%20%26%20-8%20%26%202%20%5C%5C2%20%26%20-4%20%26%201%5Cend%7Bbmatrix%7D'%3D%5Cbegin%7Bbmatrix%7D-2%20%26%204%20%26%202%20%5C%5C4%20%26%20-8%20%26%20-4%20%5C%5C-1%20%26%202%20%26%201%5Cend%7Bbmatrix%7D$

Thus, the correct answer is:

$%5Cbegin%7Bbmatrix%7D-2%20%26%204%20%26%202%20%5C%5C4%20%26%20-8%20%26%20-4%20%5C%5C-1%20%26%202%20%26%201%5Cend%7Bbmatrix%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Product Of Matrices

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs