Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2…
The following solution is suggested to handle the subject “Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2…“. Let’s keep an eye on the content below!
Question “Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2…”
Answer
Answer:
Data provided:
It is necessary to determine if the columns in the matrix form a linearly-independent set.
To determine if the columns in the matrix form a linearly-independent set, we must solve the equation given below.
The augmented matrix can be written as follows:
Let’s now reduce the matrix to the row-echelon reduced form.
We get the following results from
by interchanging row1 with row3.
, we get –
, we get –
, we get –
, we get –
, we get –
, we get –
, we get –
, we get –
, we get –
The matrix above is in reduced row-echelon format.
equation has a trivial solution.
If A is the given matrix, then the augmented
This matrix’s reduced row-echelon form indicates that Ax=0 only has the trivial solution.
The columns of A are therefore a linearly dependent set.
Therefore, the best option is (D).
Conclusion
Above is the solution for “Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2…“. We hope that you find a good answer and gain the knowledge about this topic of math.