2. Determine whether the three vectors

In $R^4$ are linearly independent. Can they form a basis of $R^4$? Why?

In $R^4$ are linearly independent. Can they form a basis of $R^4$? Why?

Determine whether the four vectors

In $R^4$ can span $R^4$. Can they form a basis of $R^4$? Why?

In $R^4$ can span $R^4$. Can they form a basis of $R^4$? Why?

4. Find the transition matrix from the basis $E$ of $R^4$

to the basis $F$ of $R^4$

to the basis $F$ of $R^4$

Find the rank of the $4 \times 5$ matrix

6. Find the matrix representing the linear transformation

with respect to the standard basis of $R^4$ and the following basis of $R^3$

with respect to the standard basis of $R^4$ and the following basis of $R^3$

7. Find the matrix representing the linear transformation

with respect to the standard basis of $R^4$.

with respect to the standard basis of $R^4$.

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