Matrix exercise

1. Exercise 1


  1. If number of elements in a matrix is 60 then how many different order of matrix are possible -
    (A) 12
    (B) 6
    (C) 24
    (D) none of these
  2. If  for the matrices
    and then  is
    (A) an odd multiple of 
    (B) an odd multiple of 
    (C) an even multiple of 
    (D) 0
  3. If , then  is equal to -
    (A) 
    (B) 
    (C) 
    (D) none of these
  4.  is a (  ) diagonal matrix having integral entries such that , number of such matrices is
    (A) 360
    (B) 390
    (C) 240
    (D) 270
  5. If the product of  matrices is equal to the matrix then the value of  is equal to -
    (A) 26
    (B) 27
    (C) 377
    (D) 378
  6. Matrix A has  rows and columns. Matrix  has  rows and  columns. Both  and exist, then -
    (A) 
    (B) 
    (C) 
    (D) 
  7. If , then 
    (A) 
    (B) diag 
    (C) 
    (D) B
  8. If  and , then matrix  is equal to -
    (A) 
    (B) 
    (C) 
    (D) 
  9. Matrix  is such that , where  is the identity matrix. The for 
    (A) 
    (B) 
    (C) 
    (D) 
  10. If  and , then -
    (A) 
    (B) 
    (C) 
    (D) 
  1. If  is a skew symmetric matrix such that , then  is equal to -
    (A) 
    (B) I
    (C) - I
    (D) 
  2. Suppose  is a matrix such that  and , then  is
    (A) 127
    (B) 511
    (C) 1023
    (D) 1024
  3. Which of the following is an orthogonal matrix -
    (A) 
    (B) 
    (C) 
    (D) 
  4. Given . If  is a singular matrix then
    (A) 
    (B) 
    (C) 
    (D) 
  5. If  is an orthogonal matrix , then  is equal to -
    (A) 
    (B) 
    (C) 
    (D) 
  6. If and , then equals -
    (A) 
    (B) 
    (C) 
    (D) 
  7.  is an involutary matrix given by  then the inverse of  will be
    (A) 
    (B) 
    (C) 
    (D) 
  8.  and  are two given matrices such that the order of  is , if  and  are both defined then
    (A) order of  is 
    (B) order of  is 
    (C) order of  is 
    (D) B'A is undefined
  9. If  and , then 
    (A) 0
    (B) 
    (C) 
    (D)