Chapter 1, Problem 1RE

To determine

Whether the statement “ If B is a $3\times 4$ matrix, then its column are $1\times 3$ vectors”.

Answer to Problem 1RE

The statement is $\underset{\_}{\text{False}}$.

Explanation of Solution

Consider the given statement as “ If B is a $3\times 4$ matrix, then its column are $1\times 3$ vectors”.

Here, the order of the matrix is $3\times 4$ and its general form is $\left[\begin{array}{cccc}{a}_1& b_1& c_1& d_1\\ a_2& b_2& c_2& d_2\\ a_3& b_3& c_3& d_3\end{array}\right]$.

From the matrix, it is noticed that the columns of $3\times 4$  matrix are of the form ${\left[\begin{array}{c}a\\ b\\ c\end{array}\right]}_{3\times 1}$.

Hence, the order of the every column of the matrix of order $3\times 4$ is $3\times 1$.

Hence, the statement is $\underset{\_}{\text{False}}$.