if f(x)= | a -1 0 | - Maths - Determinants

Question

Ishwarmani · Accepted Answer

Dear
Student,
Please
find below the solution to the asked query:

We have,fx=a-10axa-1ax2axa⇒fx=a1-10xa-1x2axaApplying C1→C1+C2⇒fx=a0-10x+aa-1x2+axaxa⇒fx=a0-10x+aa-1xx+aaxa⇒fx=ax+a0-101a-1xaxaNow, expanding along R1, we get⇒fx=ax+a1a+x⇒fx=ax+a2Also, f2x=a2x+a2So, f2x-fx=a2x+a2-ax+a2                           =a2x+a2-x+a2                           =a2x+a+x+a2x+a-x+a                           =a3x+2ax                           =ax3x+2a∴ f2x-fx=ax3x+2a

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if f(x)= | a -1 0 | | ax a -1| | ax2 ax a| using properties of determinants find the value of f(2x) -f(x)

if f(x)= | a -1 0 |
| ax a -1|
| ax² ax a|
using properties of determinants find the value of f(2x) -f(x)