MATH 2660

Midterm 2 | Spring '11

1. Determine whether the set Is a space of $R^3$

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2. Determine whether the three vectors


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

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Determine whether the four vectors


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

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


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


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



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6. Find the matrix representing the linear transformation


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


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7. Find the matrix representing the linear transformation


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


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