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MathsHardMCQ2024 · 04 Apr Shift 2

Q71.Let A = [ 10 21 ] and B = I + adj(A) + (adj A)2 + … + (adj A)10 . Then, the sum of all the elements of the matrix B is: (1) -124 (2) 22 (3) -88 (4) -110

What This Question Tests

This problem involves calculations related to adjoint of a matrix and summing a geometric progression of matrices. It tests understanding of properties like det(adj(A)) and the sum formula for a matrix GP.

Concepts Tested

Determinant of a matrixAdjoint of a matrixProperties of adjointGeometric Progression (sum of terms)Matrix addition

Formulas Used

det(A)

adj(A) = C^T

adj(A) = det(A) A⁻¹

Sum of GP: S_n = a(r^n - 1)/(r - 1)

Properties of determinant of powers of adjoint

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📋 Question Details

Chapter
Matrices
Topic
Adjoint of a matrix and geometric progression
Year
2024
Shift
04 Apr Shift 2
Q Number
Q71
Type
MCQ
NCERT Ref
Class 12 Mathematics Ch 3: Matrices

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