What would you like to understand?

The set is considered a subspace because vectors of the form (x,0,−x) stay in the same form after addition or scalar multiplication. This set is the span of (1,0,−1), a line through the origin.

Conditions: The vectors are of the form (x,0,-x).; The operation is vector addition or scalar multiplication.

The set is considered a subspace because vectors of the form (x,0,−x) stay in the same form after addition or scalar multiplication. This set is the span of (1,0,−1), a line through the origin.

Conditions: The vectors are of the form (x,0,-x).; The operation is vector addition or scalar multiplication.

Subtraction is equivalent to adding the additive inverse. In matrix algebra, multiplying a matrix by the scalar -1 creates its additive inverse.

Conditions: Scalar multiplication by -1 is defined entrywise.; Matrix addition is defined entrywise.; A and B have the same dimensions.

Subtraction is equivalent to adding the additive inverse. In matrix algebra, multiplying a matrix by the scalar -1 creates its additive inverse.

Conditions: Scalar multiplication by -1 is defined entrywise.; Matrix addition is defined entrywise.; A and B have the same dimensions.