Solve a Matrix-vector equation with Solve instead of LinearSolve?

Questions
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1

Hey guys, I’m currently stuck on this one task where I’m trying to calculate how many solutions the equation A * B = X has, where A is a 3x3 matrix, and B is a 1x3 vector. I’m supposed to use Solve as a command, but I can’t get it to work unless I’m using LinearSolve. So far, I’ve got the code:

LinearSolve[( {
   {1, 1, -2},
   {3, 4, -3},
   {1, 2, 1}} ),
   {1, 1, -1}]

Where the (1,1,1) is my vector. This gave me the correct solution, but I’m supposed to use the Solve command instead, and I have no idea how to. I’d be very greatful if you could help me out with this.

2

Solve wants equations using explicit variables. That can be done along the lines below.

mat = {{1, 1, -2}, {3, 4, -3}, {1, 2, 1}};
b = {1, 1, -1};
vars = Array[x, 3];

In[30]:= mat.vars == b

(* Out[30]= {x[1] + x[2] - 2 x[3], 3 x[1] + 4 x[2] - 3 x[3], 
  x[1] + 2 x[2] + x[3]} == {1, 1, -1} *)
3

What specifically is this command for? i don’t quite understand what it means.

vars = Array[x, 3];
arnoudb (Arnoud Buzing) 4

search.gif

arnoudb (Arnoud Buzing) 5

search-2.gif

6

Jhn,

You can find all Wolfram Language functions documented online at:

and in-product (e.g in Mathematica) by pressing F1 and searching for the relevant function.

You can also select any function and press F1 to get usage help on that function.

7

Here is a nice video on solving equations in the Wolfram Language:

Another one, with really nice background music!

8

Here is another quick video!

Hope this helps you!