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starreee
18.07.2020 •
Mathematics
WILL GIVE BRAINLIEST AND 25 POINTS! Which of the following statements are true? Check all that apply. A. If any row of a square matrix is zero, its determinant is zero. B. If all numbers in a matrix are equal, its determinant is zero. C. The determinant of any identity matrix is zero. D. The determinant of a matrix with all positive numbers is always positive. E. The determinant of any zero matrix is zero.
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Ответ:
Option A, B and E
Step-by-step explanation:
Determinant = ad-bc
Let's look at the picture and solve all
Option A)
If the row ( c and d ) is zero, the determinant will be zero
=> a(0)-b(0)
=> 0-0
=> 0 (So, True)
Option B)
If a = b = c = d (Let's say 1), the determinant will be
=> (1)(1)-(1)(1)
=> 1-1
=> 0 (So, True)
Option C)
An Identity matrix is
=>![\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]](/tpl/images/0709/0132/d5c63.png)
So , it's determinant will be
=> (1)(1)-(0)(0)
=> 1-0
=> 1 (So, False)
Option D)
The determinant with matrix will all positive numbers can be negative as well as positive. This is not necessary that it would be positive. (So, False)
Option E)
A zero matrix is
=>![\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]](/tpl/images/0709/0132/9aa24.png)
So, it's determinant is:
=> (0)(0)-(0)(0)
=> 0-0
=> 0 (So,True)
Ответ:
Step-by-step explanation:
$5×1.09 = $5.45