December 29th, 2018, 06:07 PM  #1 
Newbie Joined: Dec 2018 From: Japan Posts: 2 Thanks: 0  Matrix Problem
A is 2 x 3 B is x x 4 C is y x z Find the values of x,y, and z such that: i)The matrix operation ABC is a square matrix. ii)The operation AB + C is possible. 
December 29th, 2018, 06:22 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 
in general if $M_1$ is $j \times k$ and $M_2$ is $m \times n$ then in order for $M_1 M_2$ to be a valid operation $k = m$ and $M_1 M_2$ will be $j \times n$ in order form $M_1 + M_2$ to be a valid operation $j=m,~k=n$ $A:2 \times 2$ $B:x \times 4$ $C:y \times z$ $ABC \Rightarrow (2\times2)(x \times 4)(y \times z)$ given what's stated above it should be pretty easy to come up with the values of $x,~y,~z$ to make $ABC$ valid and result in a square matrix. for the 2nd question we note that the dimensions of $AB$ are easily determined once the proper value of $x$ is selected. Those dimensions dictate the values of $y,~z$ 
December 29th, 2018, 07:48 PM  #3 
Newbie Joined: Dec 2018 From: Japan Posts: 2 Thanks: 0 
Thanks for your reply. I'm quite new in mathematics. If you don't mind, would you explain how to get the answers for i) and ii)? cheers 
December 29th, 2018, 08:22 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402  Quote:
The only further assistance I could provide you on this problem is to simply tell you the answers. I'm not going to do that.  

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