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What does it mean when a matrix is invertible? (Choose all correct answers)Question 11Select one or more:a.the linear transformation represented by the matrix cannot be undoneb.the matrix has an inversec.the linear transformation represented by the matrix can be undoned.the determinant is not zeroe.the determinant is zerof.the matrix does not have an inverse

Question

What does it mean when a matrix is invertible? (Choose all correct answers)Question 11Select one or more:a.the linear transformation represented by the matrix cannot be undoneb.the matrix has an inversec.the linear transformation represented by the matrix can be undoned.the determinant is not zeroe.the determinant is zerof.the matrix does not have an inverse

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Solution

The correct answers are:

b. The matrix has an inverse: An invertible matrix is one that has an inverse. This means there exists another matrix such that when the two are multiplied together, the result is the identity matrix.

c. The linear transformation represented by the matrix can be undone: This is another way of saying that the matrix has an inverse. If a matrix represents a linear transformation, then its inverse represents the "reverse" transformation.

d. The determinant is not zero: This is a key property of invertible matrices. If the determinant of a matrix is zero, then the matrix is not invertible. Conversely, if the determinant is not zero, then the matrix is invertible.

So, the correct options are b, c, and d.

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Consider the matrix . Which of the following statements is correct?Question 1Select one:Select one:a.None of the other statements are correct.b.The matrix is invertible and its determinant is not equal to zero.c.The matrix is not invertible and its determinant is not equal to zero.d.The matrix is not invertible and its determinant is equal to zero.e.The matrix is invertible and its determinant is equal to zero.

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