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Problem 9. (5 points) Determine whether the following statements are true or false. All vectors are in $\mathbb{R}^n$. 1. Every orthogonal set in $\mathbb{R}^n$ is a linearly independent set. 2. If a set $S = \{u_1, \dots, u_p\}$ has the property that $(u_i, u_j) = 0$ whenever $i \neq j$, then $S$ is an orthonormal set. 3. A square matrix with orthonormal columns is invertible. 4. If $Q$ is an $m \times n$ matrix with orthonormal columns, then $Q^TQ = I_n$, the $n \times n$ identity matrix. Note: You can earn partial credit on this problem.

          Problem 9. (5 points)
Determine whether the following statements are true or false. All vectors are in $\mathbb{R}^n$.
1. Every orthogonal set in $\mathbb{R}^n$ is a linearly independent set.
2. If a set $S = \{u_1, \dots, u_p\}$ has the property that $(u_i, u_j) = 0$ whenever $i \neq j$, then $S$ is an orthonormal set.
3. A square matrix with orthonormal columns is invertible.
4. If $Q$ is an $m \times n$ matrix with orthonormal columns, then $Q^TQ = I_n$, the $n \times n$ identity matrix.
Note: You can earn partial credit on this problem.

$Problem 9. (5 points) Determine whether the following statements are true or false. All vectors are in ℝ^n. 1. Every orthogonal set in ℝ^n is a linearly independent set. 2. If a set S = {u1, …, up} has the property that (ui, uj) = 0 whenever i ≠ j, then S is an orthonormal set. 3. A square matrix with orthonormal columns is invertible. 4. If Q is an m × n matrix with orthonormal columns, then Q^TQ = In, the n × n identity matrix. Note: You can earn partial credit on this problem.$

Added by Christina H.

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