Let A = a 1 a 2 and B = b 1 b 2 be two 2 × 1 matrices with real entries such that A = X B , where X = 1 3 1 - 1 1 k , and k ∈ R . If a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 and k 2 + 1 b 2 2 ≠ - 2 b 1 b 2 , then the value of k is

Question

Let A = a 1 a 2 and B = b 1 b 2 be two 2 &#215; 1 matrices with real entries such that A = X B , where X = 1 3 1 - 1 1 k , and k &#8712; R . If a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 and k 2 + 1 b 2 2 &#8800; - 2 b 1 b 2 , then the value of k is __________.

Quantrex Academy · Accepted Answer

Correct answer: 0

A = X B a 1 a 2 = 1 3 1 - 1 1 k b 1 &#160; b 2 3 a 1 3 a 2 = b 1 - b 2 &#160; b 1 + k b 2 b 1 - b 2 = 3 a 1 &#160; &#8230; 1 b 1 + k b 2 = 3 a 2 &#160; &#8230; 2 Given, a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 ( 1 ) 2 + ( 2 ) 2 b 1 + b 2 2 + b 1 + k b 2 2 = 3 a 1 2 + a 2 2 a 1 2 + a 2 2 = 2 3 b 1 2 + 1 + k 2 3 b 2 2 + 2 3 b 1 b 2 k - 1 Given, a 1 2 + a 2 2 = 2 3 b 1 2 + 2 3 b 2 2 On comparing we get k 2 + 1 3 = 2 3 &#8658; k 2 + 1 = 2 &#8658; k = &#177; 1 &#160; &#8230; 3 2 3 ( k - 1 ) = 0 &#8658; k = 1 &#160; &#8230; 4 F

Let A = a 1 a 2 and B = b 1 b 2 be two 2 × 1 matrices with real entries such that A = X B , where X = 1 3 1 - 1 1 k , and k ∈ R . If a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 and k 2 + 1 b 2 2 ≠ - 2 b 1 b 2 , then the value of k is __________.

Correct answer

Step-by-step solution

More from Matrices

Let A = a 1 a 2 and B = b 1 b 2 be two 2 &#215; 1 matrices with real entries such that A = X B , where X = 1 3 1 - 1 1 k , and k &#8712; R . If a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 and k 2 + 1 b 2 2 &#8800; - 2 b 1 b 2 , then the value of k is __________.

Correct answer

Step-by-step solution

More from Matrices

Let A = a 1 a 2 and B = b 1 b 2 be two 2 × 1 matrices with real entries such that A = X B , where X = 1 3 1 - 1 1 k , and k ∈ R . If a 1 2 + a 2 2 = 2 3 b 1 2 + b 2 2 and k 2 + 1 b 2 2 ≠ - 2 b 1 b 2 , then the value of k is __________.