 Suppose A and B are two non singular matrices such that B \neq I, | Filo  Class 12

Math

Algebra

Determinants 585

Suppose and are two non singular matrices such that and . Find the least value of for .

1. 63
Solution:
Step 1: Given:

Step 2: To find:
Value of for which

Step 3: Formula used:

Step 4: Solution:
Consider the given expression
... (1)

Step 5: Aim to make RHS as independent of
Pre-multiply (1) from both sides by , we get
Post-multiply above equation from both sides by , we get
Since, it is given that
Expression (3) reduces to
Pre-multiply this on both sides by , we get

.....(2)

Step 8:
Now substituting the value of from (2) in LHS of (2) itself, we get
Since, we know
... (3)

Step 9:
Now substituting the value of from (2) in LHS of (3), we get

Since, we know
...(4)

Step 10:
Looking at the pattern of (2), (3) and (4), we can say that
is increasing by
is forming a GP as , and
is decreasing by
In the same manner, we find that when , we get and
So, the expression becomes
Since, we know
...(5)

Step 11:
Now, we have
Post-Multiplying this by both sides, we get
... (6)
Since, , (6) reduces to
.... (7)

Step 12:
Comparing (7) with the given condition where , we find that

Step 13: Result: 585 Connecting you to a tutor in 60 seconds.