Are these sets of equations linear? What is the number of variables and equations in each system? Please correct me if my answer is wrong:

a) $Ax=b,x\in {R}^{n}$ - yes, classic system of linear equations, $var=n,eq=m$ where $A\in {R}^{m\times n}$

b) ${x}^{T}Ax=1,x\in {R}^{n}$ - no, its a quadratic form, $var=n,eq=1$

c) ${a}^{T}Xb=0,X\in {R}^{m\times n}$ - yes, $var=m\ast n,eq=1$

d) $AX+X{A}^{T}=C,X\in {R}^{m\times n}$ - yes, not sure

a) $Ax=b,x\in {R}^{n}$ - yes, classic system of linear equations, $var=n,eq=m$ where $A\in {R}^{m\times n}$

b) ${x}^{T}Ax=1,x\in {R}^{n}$ - no, its a quadratic form, $var=n,eq=1$

c) ${a}^{T}Xb=0,X\in {R}^{m\times n}$ - yes, $var=m\ast n,eq=1$

d) $AX+X{A}^{T}=C,X\in {R}^{m\times n}$ - yes, not sure