Range and Null Space of a Matrix

Practice Questions

Linear Algebra › Range and Null Space of a Matrix

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Calculate the Null Space of the following Matrix.

$A=\left[\begin{matrix} 1 & 1& 1& -1 \ 2 & 4&5 &6 \ 3& 9& 5& 4 \end{matrix}\right]$

Find the null space of the matrix operator $T_M = \begin{bmatrix} 1 &1 & 0\ 0& -1& 1\ 9& 0& 1\end{bmatrix}$ .

$C(-\infty , \infty)$ , the set of all continuous real-valued functions defined on $(-\infty, \infty)$ , is a vector space under the usual rules of addition and scalar multiplication.

Let be the set of all functions of the form

$f(x) = \left{\begin{matrix} 0,& x< 0\ nx,& x \ge 0 \end{matrix}\right.$

True or false: is a subspace of $C(-\infty , \infty)$ .

Find the null space of the matrix $A = \begin{bmatrix} 2 & 0& 0\1 &0 &0 \9 &8 &2 \end{bmatrix}$ .

$C(-\infty , \infty)$ , the set of all continuous functions defined on $(-\infty, \infty)$ , is a vector space under the usual rules of addition and scalar multiplication.

True or false: The set of all functions of the form

where is a real number, is a subspace of $C(-\infty , \infty)$ .

A matrix with five rows and four columns has rank 3.

What is the nullity of ?

$C(-\infty , \infty)$ , the set of all continuous functions defined on $(-\infty, \infty)$ , is a vector space under the usual rules of addition and scalar multiplication.

True or false: The set of all functions defined on $(-\infty, \infty)$ with inverses is a subspace of $C(-\infty , \infty)$ .

$C(-\infty , \infty)$ , the set of all continuous real-valued functions defined on $(-\infty, \infty)$ , is a vector space under the usual rules of addition and scalar multiplication.

Let be the set of all functions of the form

$f(x) = \left{\begin{matrix} 2nx+2n , & x \le - 1 \ 0, & -1 < x < 1\ -nx+n & x \ge 1 \end{matrix}\right.$