matrix{{0, 1, -1}, {2, 1, 3}, {1, 1, 1}} matrix{{1, -1, x}} matrix{{0}, {1}, {1}}=0
Find the value of x
Don't give me the direct answer. Please tell me how to go about this. Draw in your notebook and then solve
Your matrix notation does not distinguish rows from columns, which is critical in matrices.
The best possible interpretation I get is:
a11 a12 a13
a21 a22 a23
a31 a32 a33
multiplied by
b1
b2
b3
to give
c1 c2 c3
which is then multiplied by another
d1
d2
d3
to give
e=0
So multiply rows of a to the column b to give c, for example:
c1=a11*b1+a12*b2+a13*b3
and similarly for the other rows.
Same for e:
e=c1*d1+c2*d2+c3*d3
Through the multiplication, you will preserve the value of x, and equate the value of e to zero to solve for x.
To find the value of x in the equation matrix{{0, 1, -1}, {2, 1, 3}, {1, 1, 1}} matrix{{1, -1, x}} matrix{{0}, {1}, {1}} = 0, we need to perform matrix multiplication.
Let's go step by step:
1. Write down the first matrix:
| 0 1 -1 |
| 2 1 3 |
| 1 1 1 |
2. Write down the second matrix:
| 1 -1 x |
3. Write down the third matrix:
| 0 |
| 1 |
| 1 |
4. To perform matrix multiplication, we need to take the dot products of the rows of the first matrix with the columns of the second matrix. So, take the first row of the first matrix and multiply it with each column of the second matrix:
| 0 1 -1 | | 1 | | 0(1) + 1(-1) + (-1)(x) |
| | -1 | = | 2(1) + 1(-1) + 3(x) |
| | x | | 1(1) + 1(-1) + 1(x) |
5. Simplify the expressions:
| 0 1 -1 | | 1 | | -1 - x |
| | -1 | = | 2 + 3x |
| | x | | 1 + x |
6. Take the dot product of the resulting matrix with the third matrix:
| -1 - x | | 0 | | (-1 - x)(0) |
| | 1 | = | (2 + 3x)(1) |
| | 1 | | (1 + x)(1) |
7. Simplify the expressions:
| -1 - x | | 0 | | 0 |
| | 1 | = | 2 + 3x |
| | 1 | | 1 + x |
8. Set the final matrix equal to zero and solve for x:
0 = 0
2 + 3x = 0
1 + x = 0
Now, solve the equations to find the value of x.