Suppose λ is an eigenvalue of the n×n matrix A. If u and v are eigenvectors of A corresponding to λ, which of the following statement MUST be false? 1)λ=0 2) u and v are scalars multiple of each other. 3) nullity (A−λI)=0 4) 7v−3u is also an eigenvector of A.

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Suppose λ is an eigenvalue of the n×n matrix A. If u and v are eigenvectors of A corresponding to λ, which of the following statement MUST be false?  1)λ=0  2) u and v are scalars multiple of each other.  3) nullity (A−λI)=0  4) 7v−3u is also an eigenvector of A.

broliY · Accepted Answer

Step 1 In the question we have to find falsa statement. Step 2 Result - option d Given that u and v are eigen vectors of A(n×n) matrix. a) λ=0 - true eigen values can be zero or non zero or positive or negative too. b) u and v are scalar multiple of each other - true because eigen vactor are written as [1,3]t or any quantity which implies eigen vectors are scalar multiples. c) nullity A−λI=0 - true as eigen values are found by putting eigen values in this form. d) 7v−3u is also a eigen vector of matrix A - false because eigen vectors can not be calculated by taking sum, difference or any calculus.

Suppose \lambda is an eigenvalue of the n \times n

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