Question

Given an n by n matrix A, prove or disprove that the set H is a subspace of $M_{n imes 1}$ H = ${x in M_{n imes 1} | AX = 7X}$ (Note: A is an n by n matrix, X is an n by 1 matrix, so AX is an n by 1 matrix, and 7X is an n by 1 matrix).

          Given an n by n matrix A, prove or disprove that the set H is a subspace of $M_{n 	imes 1}$
H = ${x in M_{n 	imes 1} | AX = 7X}$
(Note: A is an n by n matrix, X is an n by 1 matrix, so AX is an n by 1 matrix, and 7X
is an n by 1 matrix).

Given an n by n matrix A, prove or disprove that the set H is a subspace of Mn imes 1
H = x in Mn imes 1 | AX = 7X
(Note: A is an n by n matrix, X is an n by 1 matrix, so AX is an n by 1 matrix, and 7X
is an n by 1 matrix).

Added by David G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Audrey Fong

Step 1

First, we need to check if the zero vector is in H. Let X = 0 (the zero vector), then AX = A(0) = 0 and TX = T(0) = 0. Since AX = TX, the zero vector is in H. Show more…

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M Given an n by n matrix A, prove or disprove that the set H is a subspace of nx [ H={x e M AX =TX{ nx [ (Note: A is an n by n matrix, Xis an n by 1 matrix, s0 AX is an n by matrix, and 7X is an n by 1 matrix):