If A is a 3 × 3 matrix, |A| ≠ 0 and |3A| = k|A| then write value of

1.	If A is a 3 × 3 matrix, \|A\| ≠ 0 and \|3A\| = k\|A\| then write value of k.
Answer» We are given that, Order of matrix = 3 \|A\| ≠ 0 \|3A\| = k\|A\| We need to find the value of k. In order to find k, we need to solve \|3A\|. Using property of determinants, \|kA\| = kⁿ\|A\| Where, order of A is n × n. Similarly, \|3A\| = 3³\|A\| [∵, order of A is 3] ⇒ \|3A\| = 27\|A\| …(i) As, according to the question \|3A\| = k\|A\| Using (i), ⇒ 27\|A\| = k\|A\| Comparing the left hand side and right hand side, we get k = 27 Thus, the value of k is 27.

If A is a 3 × 3 matrix, |A| ≠ 0 and |3A| = k|A| then write value of k.

Answer»

We are given that,

Order of matrix = 3

|A| ≠ 0

|3A| = k|A|

We need to find the value of k.

In order to find k, we need to solve |3A|.

Using property of determinants,

|kA| = kⁿ|A|

Where, order of A is n × n.

Similarly,

|3A| = 3³|A|

[∵, order of A is 3]

⇒ |3A| = 27|A| …(i)

As, according to the question

|3A| = k|A|

Using (i),

⇒ 27|A| = k|A|

Comparing the left hand side and right hand side, we get

k = 27

Thus, the value of k is 27.