matrix arithmetic help

Question

Determine the value(s) of x such that

[3 -6 -3] [x]

[ x 2 1] -6 -2 3 -1

-3 -2 0 2

to clarify, the [ x 2 1] is a 1*3.......the A matrix is 3*3....and what i think is b, the x -1 2 is 3*1.

x = ??

Answer 1

the two matrices are compatible for multiplication

the dimensions are rows by columns, rxc

1st matrix is a 1x 3, 2nd is 3x3 so the product matrix should be 1x3, another row matrix, not a column matrix

as long as the inside numbers are equal, the 3 and 3, then you can multiply

product matrix is: [3x-12 -3, -6x-4-2, -3x+6] = [3x-15, -6x-6, -3x+6]

but if you did treat the last column matrix as a row matrix then

3x-15= x and x = 15/2 = 7.5

-6x-6 =-1 and x= -5/6

-3x+6 =2 and x = 4/3

there is no solution for x, as the 3 equations are inconsistent

the product matrix is inconsistent with the given two matrices

there may be a misprint, typo or copying error somewhere

such as maybe the product matrix was meant to be a row matrix [x, -51, -33/2]

then x= 15/2, which is consistent with

-6x-6=-51, -6x = -45, x= -45/-6 =15/2

-3x+6=-33/2, x-2 =11/2, x = 15/2

3x-15=x, 2x=15, x=15/2

you have [x,-1, 2] just change the -1 to -51 and 2 to -33/2 and it works,solving x as 15/2

maybe a 5 and a -33 were somehow deleted

or there may be an error in one of the first two matrices

Answer 2

These matrices cannot be set equal to each other because the dimensions do not match. A (1x3) times B (3x3) gives a result C which is (1x3). A matrix C which is (1x3) cannot be equal to another matrix D which is (3x1).