MTH501 Quiz 2 2026 by Iqra Azhar

The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is

Cylindrical coordinate system is also called as___________ Spherical coordinate system. Space coordinate system. Circular coordinate system. Rectangular coordinate system. In two coordinate system, \[{\left( {\mathop P\limits_{C \leftarrow B} } \right)^{ - 1}}\] is the matrix that converts B-coordinates into B-coordinates B-coordinates into C-coordinates C-coordinates into B-coordinates C-coordinates into C-coordinates The pivot columns of a matrix \[A\] form a basis for ----------- [RowA] [ColA] The rank of the matrix (m × n) where m<n cannot be more than? m n The vectors spaces - C(-infty, +infty) are ----------

The number of parameters in the solution set of Ax = 0 if A is a 4× 4 matrix of rank 0 then nullity (A) =?

True False The dimension of the zero vector space \[\left\{ 0 \right\}\] is defined to be

[\infty\] If Coordinates vector of the polynomial \[p = {a_0} + {a_1}x + {a_2}{x_2}\] Relative to the basis S = \[\{ 1,x,{x^2}\} \,\,\,\] for \[{p_2}\] then linear combination of the basis set S is [P]_s = (a_0 + a_1 + a_2) [P]_s = [a_0 + a_1 + a_2] An indexed set of vectors \[{v_1,v_2,…,v_p}\] in \[V\] is said to be linearly independent if the vector equation \[{c_1}{v_1} + {c_2}{v_2} + \ldots + {c_p}{v_p} \ne 0\] \[{c_1}{v_1} + {c_2}{v_2} + \ldots + {c_p}{v_p} = 1\] c_1v_1}+ c_2v_2 + \ldots + {c_p}{v_p} =0\] None of the above. Any set of linearly independent vectors cannot contain the ----------- vector. Identity

zero Unit If A is any matrix, then rank (A)=rank(A^t) False True

False True Every finite dimensional vector space contains a/an Basis Empty set Infinite set None of the above If two matrices A and B are row equivalent, then their row spaces are the same.