Question: Consider linearly independent vectors in and let A be an invertible matrix. Are the columns of the following matrix linearly independent?
Yes, the columns of the matrix linearly independent.
Linearly independent is defined as the property of a set having no linear combination of its elements equal to zero when the coefficients are taken from a given set unless the coefficient of each element is zero.
are linearly independent vectors.
We are given a matrix A that is invertible.
Let’s say that
Since they are independent we know that ker B = 0
Therefore kerBA = 0 so columns of AB are linearly independent.
Yes, the columns of the matrix are linearly independent.
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