Which of the matrix equations represents the following systems of equations?

Question

-3x + 5y + z = 10

2x + 3y - z = 7

-4x + 2y +3z = -1

a. [x y z] |-3 2 -4|

...............| 5 3 2| = [ 10 7 -1]

.............. | 1 -1 3|

b.

|-3 2 -4|

| 5 3 2| [x y z] = [ 10 7 -1]

| 1 -1 3|

c. Both A and B

d Both A nor B

I thought that the correct answer was b. But I was wrong, im thinking its C

Answer 1

well the answer is a option.

here is the reason for giving a as the answer

to multiply two matrices one condition must be satisfied and i.e. the no of columns of the first matrix must be equal to the nuber of rows of the second matrix. now acc to this when u solve the above question the first matrix has an order of 1*3 and the second has an order of 3*3 so the condition is satisfied and also when u multiple them u do get the given equations as well. i hope u understood. in b option the condition ehich i stated is not being satisfied.

Answer 2

I beleive is d, because after the equal sign, they should have been in 1 by 3 matrix, not 3 by 1. But the first part in a multiplies back to the eguation, not in b. I still think it should be d.

Answer 3

It's A. In B you can't even multiply the matrices because the number of columns in the first matrix does not match the number of rows in the second one.

Answer 4

a

Answer 5

A is correct.

B is invalid as it is. You can not post-multiply a 3x3 matrix by a 1x3 vector. That and the result should be column vectors to be valid. Then it is not correct. It would be correct if you transpose the current matrix.

Answer 6

[-3  5  1]  [x]      [10]              (**)

  [2   3 -1]  [y]  =  [7 ]

  [-4  2  3]  [z]      [-1]

multiplied first line numbers with x, y, z column     => equal 10

multiplied second line numbers with x, y, z column=> equal 7

multiplied third line numbers    with x, y, z   column => equal -1

(**) is a matrix form for your equations system.