Question 1: Find , if
[2003]
Answer:
Therefore
and
Hence
Question 2: Find if:
Answer:
Therefore
and
Question 3: If and
find the value of
if i)
are whole numbers ii)
are integers.
Answer:
… … … … … … i)
… … … … … … ii)
Multiplying i) by 2 and adding it to ii) we get
If
Similarly, if
Hence if are whole numbers, then
.
If are Integers, then
.
Question 4: Given , find: i) the order of matrix
ii) the matrix
[2012]
Answer:
Therefore . Hence the order of Matrix is
Let
Therefore
Therefore
and
Solving we get
Hence
Question 5: Evaluate:
Answer:
Question 6: If ,
and
, find matrix
.
Answer:
Therefore . Hence the order of Matrix is
Let
Therefore
and
Hence
Question 7: If find the value of
. [1981]
Answer:
Therefore
Question 8: If , and
find: i)
ii)
[1991]
Answer:
i)
ii)
Question 9: Find , if
[1992, 2013]
Answer:
Therefore
and
Question 10: If the matrix and
. Find the matrix
.
Answer:
Question 11: Given ,
and
; Find
such that
. [2005]
Answer:
Question 12: Find the value of given that
,
, and
. [2005]
Answer:
Therefore
Question 13: If , and
and
matrix of the same order and
is the transpose of the matrix, find
. [2011]
Answer:
Question 14: Given ,
and
; Find the matrix
such that
. [2013]
Answer:
Question 15: Let ,
and
. Find
[2006]
Answer:
Question 16: Let ,
. Find
[2007]
Answer:
Question 17: If ,
and
and
, find the value of
.
Answer:
Therefore
Question 18: Given ,
and
and
. FInd the value of
. [2008]
Answer:
Therefore
and
Question 19: Given ,
,
and
. Find
. [2010]
Answer:
Question 20: Evaluate [2010]
Answer:
Question 21: If ,
, find
. [2012]
Answer: