Assume that the product AB makes sense. Prove that if the columns of B are linea
rabbitz42z8
Answered question
2021-11-08
Answer & Explanation
Befoodly
Beginner2021-11-09Added 17 answers
Let
where are columns of the matrix B. According to our hypothesis those columns are linearly dependent, so there are some constants such that for some . The product of
matrices A and B is then:
where the column of the matrix AB is product of the matrix A and the column of the matrix B. Now we have that:
=A(0)=0.
There exist constants such that for some , so columns of the matrix AB are linearly dependent.
Results:
Due to the linear dependence of the columns of the matrix B, there are non-trivial constants that guarantee that the result of a linear combination of those columns is 0. Show that the columns of matrix AB make a linear combination equal to 0, indicating that they are linearly dependent, by using the same constants.
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