Matrices And Determinants

To calculate the determinant of the given matrix $%5Cbegin%7Bbmatrix%7D%201%20%26%203%20%26%200%20%5C%5C%202%20%26%206%20%26%204%20%5C%5C%20-1%20%26%20-1%20%26%202%20%5Cend%7Bbmatrix%7D$ , we apply the formula for a 3x3 matrix determinant:

$%5Ctext%7Bdet%7D(A)%20%3D%20a(ei%20%E2%88%92%20fh)%20%E2%88%92%20b(di%20%E2%88%92%20fg)%20%2B%20c(dh%20%E2%88%92%20eg)$

Assigning values from the matrix:

$a%20%3D%201$ , $b%20%3D%203$ , $c%20%3D%200$
$d%20%3D%202$ , $e%20%3D%206$ , $f%20%3D%204$
$g%20%3D%20-1$ , $h%20%3D%20-1$ , $i%20%3D%202$

Substitute these values into the formula:

$ei%20-%20fh%20%3D%20(6%20%5Ctimes%202)%20-%20(4%20%5Ctimes%20-1)%20%3D%2012%20%2B%204%20%3D%2016$
$di%20-%20fg%20%3D%20(2%20%5Ctimes%202)%20-%20(4%20%5Ctimes%20-1)%20%3D%204%20%2B%204%20%3D%208$
$dh%20-%20eg%20%3D%20(2%20%5Ctimes%20-1)%20-%20(6%20%5Ctimes%20-1)%20%3D%20-2%20%2B%206%20%3D%204$

Thus,

$%5Ctext%7Bdet%7D(A)%20%3D%201%20%5Ctimes%2016%20-%203%20%5Ctimes%208%20%2B%200%20%5Ctimes%204$

Calculate:

$%5Ctext%7Bdet%7D(A)%20%3D%2016%20-%2024%20%3D%20-8$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Matrices And Determinants

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs