Question

Drag each tile to the correct box.

Answer 1

Answer:

Order of the Matrix will be

$\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right]$  

↓

$\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right]$  

↓

$\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right]$

Step-by-step explanation:

Given - The matrices are -

$\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right]$

$\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right]$

$\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right]$

$\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right]$

$\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right]$

$\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right]$

$\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right]$

To find - Arrange the matrices in increasing order of their determinant values.

Proof -

Determinant of matrix $\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right]$ is

= (2)(4) - (6)(3)

= 8 - 18

= -10

So,

Determinant of matrix $\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right]$  = -10

Determinant of matrix $\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right]$ is

= (-2)(9) - (-7)(5)

= -18 + 35

= 17

So,

Determinant of matrix $\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right]$ = 17

Determinant of matrix $\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right]$ is

= (6)(-8) - (6)(5)

= -48 - 30

= -78

So,

Determinant of matrix $\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right]$  = -78

Determinant of matrix $\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right]$ is

= (2)(-5) - (4)(5)

= -10 - 20

= -30

So,

Determinant of matrix $\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right]$ = -30

Determinant of matrix $\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right]$ is

= (2)(4) - (5)(-2)

= 8 + 10

= 18

So,

Determinant of matrix $\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right]$ = 18

Determinant of matrix $\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right]$ is

= (4)(2) - (-3)(5)

= 8 + 15

= 23

So,

Determinant of matrix $\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right]$  = 23

Determinant of matrix $\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right]$ is

= (3)(6) - (2)(4)

= 18 - 8

= 10

So,

Determinant of matrix $\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right]$  = 10

Now,

Increasing order of Determinant is -

-78 < -30 < -10 < 10 < 17 < 18 < 23

So,

Order of the Matrix will be

$\left[\begin{array}{ccc}6&6\\5&-8\\\end{array}\right]$  

↓

$\left[\begin{array}{ccc}2&4\\5&-5\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}2&6\\3&4\\\end{array}\right]$  

↓

$\left[\begin{array}{ccc}3&2\\4&6\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}-2&-7\\5&9\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}2&5\\-2&4\\\end{array}\right]$

↓

$\left[\begin{array}{ccc}4&-3\\5&2\\\end{array}\right]$