Question

If 2 3 4 are the eigenvalues of a then the eigenvalues of 4a will be

Answer 1

Step-by-step explanation:

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Answer 2

If 2, 3, 4 are the eigenvalues of a then the eigenvalues of 4a will be 8, 12, 16.

• Consider a square matrix A, such that for some scalar k, $AX = kX.$ Where, X is a non-zero column vector. Then k will be called an eigenvalue of the matrix A and X is an eigenvector of matrix A associated with k.
• Now, the eigenvalues of a matrix get multiplied by the same scalar 's' when a matrix is multiplied by a scalar 's'. In other words, e.g. if 'k' is an eigenvalue of a matrix A, then 'sk' will be the eigenvalue of the matrix sA.
• Therefore, here, as the matrix is being multiplied by 4, so all its eigenvalues will also be multiplied by 4. So, the resulting eigenvalues will be 8 (= 2×4), 12 (= 3×4), and 16 (= 4×4).