Question

The Set of all solutions of AX = 0 is ----
Options
O Col A
O rank (A)
O Nul A
O range of A

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Answer 1

Answer:

The set of all solutions of AX=0 is COL A

Answer 2

Concept:

This question is related to the concept of subspace associated with matrix of a vector space.

A non empty subset W of a vector space V over a field F is called a subspace if W is a Vector Space itself  over F with respect to same composition Vector Addition and Scalar  Multiplication.

Solution:

The set of all solutions  of homogeneous system of equations is called the Nullspace of an m × n matrix A.

Mathematically, Null A={X | X in $R^{n}$ and AX=0}

Hence, The set of all solutions of AX=0 is Null A.

Option (c) is the correct choice.