Question

There exists an invertible matrix of the form

$\left[\begin{array}{cccc}a& e& f& j\\ b& 0& g& 0\\ c& 0& h& 0\\ d& 0& i& 0\end{array}\right]$

Short answer

Therefore, the given condition is not satisfied. So, the given statement is false..

Step-by-step solution

Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “ $m\times n$.”

Given. 

Given matrix,

$\left[\begin{array}{cccc}a& e& f& j\\ b& 0& g& 0\\ c& 0& h& 0\\ d& 0& i& 0\end{array}\right]$

To check whether the given condition is true or false.

The fourth row of given matrix can always be obtained as a linear combination of the second and third row.

Therefore, the given condition is not satisfied. So, the given statement is false.