Which matrix can be multiplied to the left of a vector matrix to get a new vector matrix ?

 The answer is (B).

Step-by-step explanation:  We are given four options and we are to select which matrix can be multiplied to the left of a vector matrix to get a new vector matrix. The order of a vector matrix is either n × 1  or  1 × n.

For (A): The order of the matrix is 2 × 1. If we multiply this matrix by a vector matrix of order 1 × 2, then the resulting matrix will be of order 2 × 2, which is not a vector matrix.

For (B): The order of the matrix is 3  × 2. If we multiply this matrix by a vector matrix of order 2 × 1, then the resulting matrix will be of order 3 × 1, which is a new vector matrix.

For (C): The order of the matrix is 2  × 2. If we multiply this matrix by a vector matrix of order 2 × 1, then the resulting matrix will be of order 2 × 1, which is a vector matrix of order same as before.

For (D): The order of the matrix is 1  × 2. If we multiply this matrix by a vector matrix of order 2 × 1, then the resulting matrix will be of order 1 × 1, which is a not vector matrix.

Thus, the correct option is (B).

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step-by-step explanation: