Q85.Let I be an identity matrix of order 2 × 2 and P = [25 −1−3 ] P n = 5I −8P is equal to ___ .
What This Question Tests
The problem asks for a relation involving P^n and requires finding the characteristic equation of the matrix P using the Cayley-Hamilton Theorem. This allows expressing higher powers of P in terms of P and I, simplifying the calculation.
Concepts Tested
Formulas Used
P^2 - (Tr(P))P + det(P)I = 0
P^n = aP + bI (for 2x2 matrix)
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
📋 Question Details
- Chapter
- Matrices
- Topic
- Powers of a matrix and Cayley-Hamilton Theorem
- Year
- 2021
- Shift
- 18 Mar Shift 2
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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