Let P = 3 - 1 - 2 2 0 α 3 - 5 0 , where α ∈ R , Suppose Q = q i j is a matrix such that P Q = k I , where k ∈ R , k ≠ 0 and I is the identity matrix of order 3. If q 23 = - k 8 and det ⁡ Q = k 2 2 then

Question

Let P = 3 - 1 - 2 2 0 &#945; 3 - 5 0 , where &#945; &#8712; R , Suppose Q = q i j is a matrix such that P Q = k I , where k &#8712; R , k &#8800; 0 and I is the identity matrix of order 3. If q 23 = - k 8 and det &#8289; Q = k 2 2 then

Quantrex Academy · Accepted Answer

Correct answer: B. 4 α - k + 8 = 0

P Q = k I P Q = k 3&#160; &#160; &#160; ( as order is 3 ) &#8658; P = 2 k &#160; &#8800; 0 &#160; &#160; &#8658; &#160; &#160; P is an invertible matrix &#8757; P Q = k I &#8756; Q = k P - 1 &#160; I = K 1 P adj P &#8756; Q = a d j . P 2 &#8757; q 23 = &#160; - k 8 ( &#8756; cofactor P 32 = - 3 &#945; + 4 ) &#8658; 12 &#945; + 16 = K &#38; adjP 2 = P 32 2 T - q 23 &#8756; undefined ...... (i) Also P = 2 k &#8658; k = 10 + 6 &#945; ......(ii) Solving these two &#8658; 12 &#945; + 16 = 10 + 6 &#945; &#8658; &#945; =

Let P = 3 - 1 - 2 2 0 α 3 - 5 0 , where α ∈ R , Suppose Q = q i j is a matrix such that P Q = k I , where k ∈ R , k ≠ 0 and I is the identity matrix of order 3. If q 23 = - k 8 and det ⁡ Q = k 2 2 then

Options

Correct answer

Step-by-step solution

More from Matrices

Let P = 3 - 1 - 2 2 0 &#945; 3 - 5 0 , where &#945; &#8712; R , Suppose Q = q i j is a matrix such that P Q = k I , where k &#8712; R , k &#8800; 0 and I is the identity matrix of order 3. If q 23 = - k 8 and det &#8289; Q = k 2 2 then

Options

Correct answer

Step-by-step solution

More from Matrices

Let P = 3 - 1 - 2 2 0 α 3 - 5 0 , where α ∈ R , Suppose Q = q i j is a matrix such that P Q = k I , where k ∈ R , k ≠ 0 and I is the identity matrix of order 3. If q 23 = - k 8 and det ⁡ Q = k 2 2 then