Let A = 1 2 - 1 4 . If A - 1 = α I + β A ,   α , β ∈ R ,   I is a 2 × 2 identity matrix, then 4 α - β is equal to :

Question

Let A = 1 2 - 1 4 . If A - 1 = &#945; I + &#946; A , &#160; &#945; , &#946; &#8712; R , &#160; I is a 2 &#215; 2 identity matrix, then 4 &#945; - &#946; is equal to :

Aicharya · Accepted Answer

Given, A = 1 2 - 1 4 &#8658; A = 6 So, A - 1 = adj A A = 1 6 4 - 2 1 1 = 2 3 - 1 3 1 6 1 6 Here, 2 3 - 1 3 1 6 1 6 = &#945; 0 0 &#945; + &#946; 2 &#946; - &#946; 4 &#946; &#945; + &#946; = 2 3 &#946; = - 1 6 &#8658; &#945; = 2 3 + 1 6 = 5 6 Hence, 4 &#945; - &#946; = 4 1 = 4

Let A = 1 2 - 1 4 . If A - 1 = α I + β A ,   α , β ∈ R ,   I is a 2…

Solution

Let A = 1 2 - 1 4 . If A - 1 = &#945; I + &#946; A , &#160; &#945; , &#946; &#8712; R , &#160; I is a 2…

Solution

Let A = 1 2 - 1 4 . If A - 1 = α I + β A , α , β ∈ R , I is a 2…