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MathsMediumNumerical2022 ยท 25 Jun Shift 2

Q85.Let ๐ด= 2 -2 and๐ต= -1 2 . Then the number of elements in the set {๐‘›, ๐‘š: ๐‘›, ๐‘šโˆˆ1, 2, โ€ฆ โ€ฆ . 10 and 1 -1 -1 2 ๐‘›๐ด๐‘›+ ๐‘š๐ต๐‘š= ๐ผ} is _____.

What This Question Tests

This question tests the understanding of matrix multiplication and powers, specifically identifying if the given matrices are idempotent or follow a specific pattern of powers, to solve a matrix equation.

Concepts Tested

Matrix multiplicationMatrix powersIdempotent matrixNilpotent matrixIdentity matrix

Formulas Used

Aยฒ = AยทA

Bยฒ = BยทB

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๐Ÿ“‹ Question Details

Chapter
Matrices
Topic
Matrix powers and properties
Year
2022
Shift
25 Jun Shift 2
Q Number
Q85
Type
Numerical
NCERT Ref
Class 12 Mathematics Ch 3: Matrices

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