Misc 8 - Chapter 3 Class 12 Matrices (Important Question)
Last updated at April 16, 2024 by Teachoo
Chapter 3 Class 12 Matrices
Ex 3.1, 9 (MCQ) Important
Example 18 Important
Example 19
Ex 3.2, 7 (i)
Ex 3.2, 12 Important
Ex 3.2, 16 Important
Ex 3.2, 17 Important
Ex 3.2, 20 Important
Example 22 Important
Ex 3.3, 4 Important
Ex 3.3, 10 (i) Important
Ex 3.3, 12 (MCQ)
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Example 25
Question 3 Important Deleted for CBSE Board 2024 Exams
Misc 6 Important
Misc 8 Important You are here
Misc 9 (MCQ)
Chapter 3 Class 12 Matrices
Last updated at April 16, 2024 by Teachoo
Misc 8 Find the matrix X so that X [■8(1&2&3@4&5&6)] =[■8(−7&−8&−9@2&4&6)] X [■8(1&2&3@4&5&6)] = [■8(−7&−8&−9@2&4&6)] X [■8(𝟏&𝟐&𝟑@𝟒&𝟓&𝟔)]_(𝟐 × 𝟑) = [■8(−𝟕&−𝟖&−𝟗@𝟐&𝟒&𝟔)]_(𝟐 × 𝟑) So X will be a × matrix Let X =[■8(𝑢&𝑤@𝑣&𝑥)]_(2 × 2) So, our equation becomes [■8(𝑢&𝑤@𝑣&𝑥)]_(2 × 2) [■8(1&2&3@4&5&6)]_(2 × 3) = [■8(−7&−8&−9@2&4&6)] [■8(𝑢(1)+𝑤(4)&𝑢(2)+𝑤(5)&𝑢(3)+𝑤(6)@𝑣(1)+𝑥(4)&𝑣(2)+𝑥(5)&𝑣(3)+𝑥(6))] = [■8(−7&−8&−9@2&4&6)] [■8(𝒖+𝟒𝒘&𝟐𝒖+𝟓𝒘&𝟑𝒖+𝟔𝒘@𝒗+𝟒𝒙&𝟐𝒗+𝟓𝒙&𝟑𝒗+𝟔𝒙)]_(𝟐×𝟑) = [■8(−𝟕&−𝟖&−𝟗@𝟐&𝟒&𝟔)]_(𝟐×𝟑) Since the matrices are equal Corresponding elements are equal u + 4w = - 7 2u + 5w = - 8 3u + 6w = - 9 v + 4x = 2 2v + 5x = 4 3v + 6x = 6 Solving (1) u + 4w = −7 u = −7 – 4w Putting value of u in (2) 2u + 5w = - 8 2(−7 – 4w) + 5w = - 8 −14 – 8w + 5w = - 8 −14 – 3w = - 8 −3w = - 8 + 14 −3w = 6 w = 6/(−3) w = –2 Now, u = – 7 – 4w Putting w = −2 u = – 7 – 4 (-2) u = – 7 + 8 u = 1 Solving (4) v + 4x = 2 v = 2 – 4x Putting value of v in (5) 2v + 5x = 4 2 (2 – 4x) + 5x = 4 4 – 8x + 5x = 4 4 – 3x = 4 −3x = 4 – 4 −3x = 0 x = 0 Putting value of x = 0 in (4) v + 4x = 2 v + 4(0) =2 v + 0 = 2 v = 2 Hence, u = 1 , v = 2 , w = − 2 & x = 0 Hence, matrix X = [■8(u&w@v&x)] = [■8(𝟏&−𝟐@𝟐&𝟎)]