4. What is the determinant of $$ A=\left(\begin{array}{ccc}2 & 0 & -2 \ 1 & 0 & 3 \ 7 & 0 & 5\end{array} ight) $$ ? $$ \begin{array}{llll} ext { A. } 20 & ext { B. } 0 & ext { C. } 16 & ext { D. } 24\end{array} $$

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4. What is the determinant of $$ A=\left(\begin{array}{ccc}2 & 0 & -2 \ 1 & 0 & 3 \ 7 & 0 & 5\end{array}ight) $$ ? $$ \begin{array}{llll}	ext { A. } 20 & 	ext { B. } 0 & 	ext { C. } 16 & 	ext { D. } 24\end{array} $$

UpStudy AI · Accepted Answer

Matrices by following steps:
- step0: Evaluate the determinant:
  $$\left[\begin{array}{rrr}{2}&{0}&{-2}\{1}&{0}&{3}\{7}&{0}&{5}\end{array}\right]$$
- step1: Use the appropriate notation:
  $$\left|\begin{array}{cc}{2}&{0}&{-2}\{1}&{0}&{3}\{7}&{0}&{5}\end{array}\right|$$
- step2: Use cofactor expansion along a column:
  $$-0\times \left|\begin{array}{cc}{1}&{3}\{7}&{5}\end{array}\right|+0\times \left|\begin{array}{cc}{2}&{-2}\{7}&{5}\end{array}\right|-0\times \left|\begin{array}{cc}{2}&{-2}\{1}&{3}\end{array}\right|$$
- step3: Multiply:
  $$-0+0-0$$
- step4: Remove 0:
  $$0$$
To find the determinant of the matrix

$$
A = \begin{pmatrix} 2 & 0 & -2 \ 1 & 0 & 3 \ 7 & 0 & 5 \end{pmatrix},
$$

we can use the property that if a matrix has a row (or column) of zeros, its determinant is zero.

In this case, the second column of the matrix $$ A $$ consists entirely of zeros. Therefore, the determinant of matrix $$ A $$ is

$$
\text{det}(A) = 0.
$$

Thus, the answer is $$ \text{B. } 0 $$.
The determinant of matrix $$ A $$ is 0.

What is the determinant of ?

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