Use the fact that |CA| = c^n|A| to evaluate the determinant...

Use the fact that $|CA| = c^n|A|$ to evaluate the determinant of the $n \times n$ matrix. $\begin{pmatrix} 4 & 0 & -28 & 0 \\ 0 & 4 & 0 & 0 \\ -8 & 0 & 4 & 0 \\ 0 & -32 & 0 & 4 \end{pmatrix}$

Transcript

00:01 Hello students we are given a matrix we need to find the determinant of a okay first of all we are supposed to do is no is we can just take 4 as common okay from each and every term so what we will get we can just observe we can even take directly 8 as common okay so we will take 8 as common from the whole matrix so now what we will get see we can get here 0 and here it will be 2 it will be minus 1 and here minus 4 okay here we can write minus 2 1 and minus 1 here same 1 minus 3 and 4 okay so here minus 1 here 2 and 1 minus 1 0 4 okay it's all about the basic term now after factorization after taking 8 as common now what we need to do we just need to get the determinant so basically we can directly say that we need to find the determinant of that particular term okay so we can apply the formula that determinant of c times of a is equal to c to the power n times of a matrix so a determinant of a okay where a is a matrix and a c is nothing but a constant number now what we need to do we just can write as determinant of a is equal to so basically c to the power n as we can see that it is a cross four matrix it means n have to be equal to four okay so what we can say eight to the power four okay and times of determinant of and we can add zero minus two or and a one and minus 1.

01:31 Okay.

01:32 Here it will be 2, 1, minus 3 and 4.

01:34 Okay, here we can say that minus 1, minus 1 and 0.

01:39 And here, minus 4, 2, minus 1 and 4.

01:43 It's all about the basic representation of the determinant.

01:46 Now, what we need to do is we just need to calculate it.

01:48 So, determinant of a is nothing but 8 to the power 4.

01:52 Okay, students and times.

01:54 What we can say directly that this term, first of all, when we skip this row and this column, we can write zero times of this co -factor okay so basically it will be automatically zero so we don't even write no two need to write it okay so times of zero minus a to the power four times of okay two and what we can do we can just skip that that row and that that row and that column okay so what we can write minus two one minus two one and minus one okay here and minus one one zero okay students here two minus four and four and four it's all about the second term.

02:32 Now what we need to do, we just need to go for the third term.

02:35 So basically, plus 8 to the power 4 times off...

Question

Use the fact that $|CA| = c^n|A|$ to evaluate the determinant of the $n \times n$ matrix. $\begin{pmatrix} 4 & 0 & -28 & 0 \\ 0 & 4 & 0 & 0 \\ -8 & 0 & 4 & 0 \\ 0 & -32 & 0 & 4 \end{pmatrix}$

Please give Ace some feedback