Answer:
This shows 3 pivot position matrixes.
Step-by-step explanation:
The given matrix is:
![\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-3&3&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%26-5%5C%5C0%264%263%5C%5C-3%263%260%5Cend%7Barray%7D%5Cright%5D)
The option D is correct for this matrix.
The matrix is invertible and the given matrix has 3 pivot positions.
The matrix is invertible if its determinant is nonzero.
Multiply the 3rd row by 1/3.we get:
![\left[\begin{array}{ccc}1&-2&-5\\0&4&3\\-1&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%26-5%5C%5C0%264%263%5C%5C-1%261%260%5Cend%7Barray%7D%5Cright%5D)
Now, add the first row with third row:
![\left[\begin{array}{ccc}0&-1&-5\\0&4&3\\-1&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%26-5%5C%5C0%264%263%5C%5C-1%261%260%5Cend%7Barray%7D%5Cright%5D)
Replace third row by first row:
![\left[\begin{array}{ccc}-1&1&0\\0&4&3\\0&-1&-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%260%5C%5C0%264%263%5C%5C0%26-1%26-5%5Cend%7Barray%7D%5Cright%5D)
This shows 3 pivot position matrixes.
Hence, a matrix is invertible and has 3 pivot positions.
Well , SCARLET has 7 letters S-C-A-R-L-E-T
so the amount of different arrangements would be 7!
= 7 x 6 x 5 x 4 x 3 x 2 x 1
= C. 5040
Hope this helps
You would subtract the atomic number from the mass weight. <span />
Answer:
25 students had soup for lunch
Step-by-step explanation:
Sandwich : soup
Of all students who purchased lunch this Thursday, 30 chose a sandwich
Let x = number of students who choose soup
Sandwich : soup = 30 : x
If the ratio of students who chose a sandwich to all of those who chose soup was 6:5
Sandwich : soup = 6 : 5
how many of the students had soup for lunch?
Equate both ratios
Sandwich : soup
30 : x = 6 : 5
30 / x = 6 / 5
Cross product
30 * 5 = x * 6
150 = 6x
Divide both sides by 6
x = 150 / 6
= 25
x = number of students who choose soup = 25 students
Answer:
See Below
Step-by-step explanation:
6 x 7 = 42
