Find the values of x and y.
Matrices..
[-4 2 3
5 3 5
2 -3 1] TIMES [2
x
5] EQUALS [9
38
y]
It is difficult for me to type the matrices in but....
The first matrix is 3x3 consisting of -4,2,3 in the first row.. 5,3,5 in the second row ......2,-3,1 in the third row... Then multiply this matrix by the other which is 3x1... One column going in order : 2,x,5..... Then equal to the other 3x1 matrix.. One column ...going down in order: 9,38,y)
I followed your description ok.
so we get:
-8 + 2x + 15 = 9
2x = 2
x = 1
10 + 3x + 25 = 38
3x = 3
x = 1 , confirming our first answer
4 - 3x + 5 = y
4-3+5=y
y = 6
So x = 1 , y = 6
Thank you, Reiny! :)
To solve for the values of x and y, we need to perform matrix multiplication.
First, let's represent the given matrices symbolically.
Matrix A:
[-4 2 3]
[ 5 3 5]
[ 2 -3 1]
Matrix B:
[2]
[x]
[5]
Matrix C:
[ 9 ]
[ 38 ]
[ y ]
To multiply two matrices, we match the dimensions of the matrices. In this case, matrix A is a 3x3 matrix, and matrix B is a 3x1 matrix.
The resulting matrix, matrix C, will have the dimensions of the previous number of rows from matrix A and the number of columns from matrix B, which is 3x1.
To obtain matrix C, we perform the following calculations:
C = A * B
= [(-4*2)+(2*x)+(3*5)]
[(5*2)+(3*x)+(5*5)]
[(2*2)+(-3*x)+(1*5)]
Simplified, this becomes:
[(-8+2x+15)]
[ (10+3x+25)]
[ ( 4-3x+ 5)]
Now, we can equate this with the given matrix C:
[(-8+2x+15)] = [ 9 ]
[ (10+3x+25)] = [ 38 ]
[ ( 4-3x+ 5)] = [ y ]
To solve for x and y, we can solve each equation separately.
From the first equation:
-8+2x+15 = 9
2x + 7 = 9
2x = 9 - 7
2x = 2
x = 1
From the second equation:
10+3x+25 = 38
3x + 35 = 38
3x = 38 - 35
3x = 3
x = 1
From the third equation:
4-3x+5 = y
-3x + 9 = y
-3(1) + 9 = y
-3 + 9 = y
y = 6
Therefore, the values of x and y are both 1.