Let P be a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Q and a 2 × 3 real mat

Step 1: Restate the data. P is a 3×3 nonzero real matrix and P = Q R with Q a 3×2 matrix and R a

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Let \( P \) be a \( 3 \times 3 \) non-null real matrix. If there exist a \( 3 \times 2 \) real matrix \( Q \) and a \( 2 \times 3 \) real matrix \( R \) such that \( P=Q R \), then (A) \( P x=0 \) has a unique solution, where \( 0 \in \mathbb{R}^{3} \) (B) there exists \( \boldsymbol{b} \in \mathbb{R}^{3} \) such that \( P \boldsymbol{x}=\boldsymbol{b} \) has no solution (C) there exists a non-zero \( b \in \mathbb{R}^{3} \) such that \( P x=b \) has a unique solution (D) there exists a non-zero \( \boldsymbol{b} \in \mathbb{R}^{3} \) such that \( P^{T} \boldsymbol{x}=\boldsymbol{b} \) has a unique solution

          Let \( P \) be a \( 3 \times 3 \) non-null real matrix. If there exist a \( 3 \times 2 \) real matrix \( Q \) and a \( 2 \times 3 \) real matrix \( R \) such that \( P=Q R \), then
(A) \( P x=0 \) has a unique solution, where \( 0 \in \mathbb{R}^{3} \)
(B) there exists \( \boldsymbol{b} \in \mathbb{R}^{3} \) such that \( P \boldsymbol{x}=\boldsymbol{b} \) has no solution
(C) there exists a non-zero \( b \in \mathbb{R}^{3} \) such that \( P x=b \) has a unique solution
(D) there exists a non-zero \( \boldsymbol{b} \in \mathbb{R}^{3} \) such that \( P^{T} \boldsymbol{x}=\boldsymbol{b} \) has a unique solution

Let P be a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Q and a 2 × 3 real matrix R such that P=Q R, then
(A) P x=0 has a unique solution, where 0 ∈ℝ^3
(B) there exists b∈ℝ^3 such that P x=b has no solution
(C) there exists a non-zero b ∈ℝ^3 such that P x=b has a unique solution
(D) there exists a non-zero b∈ℝ^3 such that P^Tx=b has a unique solution

Added by Heather M.

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