Class 12 CBSE Applied Maths Determinants Exercise 4.4

Class 12 CBSE Applied Maths Determinants Exercise 4.4

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.

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Q1. For what value of x the following matrix is singular ?

Q2. Which of the following matrices are non-singular?

Q3. Write the adjoint of the matrices :

Q4. (i) For what value of k, the matrix has no inverse?
(ii)
(iii) Write the inverse of the matrix

Q5. (i)
(ii) If A is a square matrix of order 3 and | A| =5, then find |adj A|.
(iii) If Ais a non-singular square matrix of order 3 such that |adj A| = 64, find | A |.
(iv) If Ais a square matrix of order 3 such that | A| = —2, then find |3 adj A|.
(v) If |A^-1| =5, then find the value of |A|.
(vi) If A = be such that A^-1 = kA, then find the value of k.
(vii) If A(adj A)= then find the value of |adj A|.

Q6. Without computing adj A, find | adj A | if

Q7.

Q8. (i) If A is a non-singular matrix, then show that |A^-1| = 1/|A|
(ii) If A is a matrix such that A³ = I, then show that A is invertible.
(iii) If A is a matrix such that A⁴ = I, then show that A^-1 = A³

Q9. If A = find A(adj A).

Q10. If the matrix is singular, find x.

Q11. Find the adjoint of the following matrices:

Also verify that A (adj A) = |A|I₂, = (adj A) A.

Q12. If A = find A (adj A) without calculating adj A.

Q13. Find the adjoint of the following matrices:

Also verify that A (adj A) = |A|I₃, = (adj A) A.

Q14. (i) Given A = compute A^-1 and show that 2A^-1 = 9I-A.
(ii) If A = show that A - 3I = 2(I + 3A^-1).

Q15. If A =
find the value(s) of x and y.

Q16. If A =
verify that adj (AB) = (adj B) (adj A).

Q17. Find the inverse of each of the following matrices:

Also verify that A^-1 A = I₃.

Q18. (i) Show that A = satisfies the equation A² - 3A - 7I = O and hence, find A^-1,
(ii) If A = then find the value of λ so that A² = λA - 2I. Hence, find A^-1.

Q19. (i) Find a 2 x 2 matrix B such that B
(ii) Solve the matrix equation

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