<p>Matrix X has r rows and c columns, and matrix Y has c rows and do columns, where r, c, and d are different. Which of the following statements must be false?</p>
<p>I. The product YX exists
II. The product of XY exists and has r rows and d columns
III. The product XY exists and has c rows and c columns</p>
<p>A) I only
B) II only
C) III only
D) I and II
E) I and III</p>
<p>Please let me know how you arrive at the answer, thanks</p>
<p>Matrix X has r rows and c columns, and matrix Y has c rows and do columns, where r, c, and d are different. Which of the following statements must be false?</p>
<p>I. The product YX exists
II. The product of XY exists and has r rows and d columns
III. The product XY exists and has c rows and c columns</p>
<p>A) I only
B) II only
C) III only
D) I and II
E) I and III</p>
<p>I personally got C because The Product XY exists because Matrix X is a RxC while Matrix Y is a CxD and the resulting matrix will be a RxD which makes II correct also. III is wrong though because the product XY does not make C rows/c columns matrix. I could be wrong, so if anyone knows the correct answer please post.</p>
<p>For the product of matrices A, B to exist (A.B is not the same as B.A) the number of columns of A = number of rows of B. and A.B will have rows the same number as A and columns the same number as B.
So II is correct. so B.</p>
<p>YX will not exist. (only XY will)</p>
<p>I got B as well,
because you can only multiply these two matrices in this order: (r x c)(c x d), so that the c's in the middle can get crossed out and the final matrix, the product, would have the dimensions: (r x d)</p>
<p>The question asks "Which one of the statements is FALSE!!!"</p>
<p>So, answer is I and III</p>
<p>okay, that's what I thought, but Barron's gives the answer as being B, but it's which is false, not which are true</p>
<p>yep... that is why don't trust barron's answers lol... They often confuse themselves.
B is the correct option... but not the answer this way. The answer will become E is false.</p>