Question

Find the value of k such that the rank of A 1 2 3 2 K 7 3 6 10
rank is 2
​

Answer 1

The value of K = 4

Correct question : Find the value of K such that rank of A is 2

$\displaystyle A = \begin{pmatrix} 1 & 2 & 3\\ 2 & K & 3 \\ 3 & 6 & 10 \end{pmatrix}$

Given :

$\displaystyle A = \begin{pmatrix} 1 & 2 & 3\\ 2 & K & 3 \\ 3 & 6 & 10 \end{pmatrix}$

To find :

Find the value of K such that rank of A is 2

Solution :

Step 1 of 2 :

Write down the given matrix

Here the given matrix is

$\displaystyle A = \begin{pmatrix} 1 & 2 & 3\\ 2 & K & 3 \\ 3 & 6 & 10 \end{pmatrix}$

Step 2 of 2 :

Find the value of K

Here it is given that rank of A is 2

Since A is 3 × 3 matrix such that rank of A is 2

So A must be singular matrix

∴ det A = 0

$\displaystyle \implies \begin{vmatrix} 1 & 2 & 3\\ 2 & K & 3 \\ 3 & 6 & 10 \end{vmatrix} = 0$

$\displaystyle \sf{ \implies }1(10K - 18) - 2(20 - 9) + 3(12 - 3K) = 0$

$\displaystyle \sf{ \implies }10K - 18 - 22 + 36 - 9K = 0$

$\displaystyle \sf{ \implies }K - 4 = 0$

$\displaystyle \sf{ \implies }K = 4$

Hence the required value of K = 4

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ A is a square matrix of order 3 having a row of zeros, then the determinant of A is 

https://brainly.in/question/28455441

2. If [1 2 3] B = [34], then the order of the matrix B is

https://brainly.in/question/9030091

#SPJ2