Questions tagged 'Linear Algebra'
5 questions
Find the value for k for which the matrix?
Find the value of k for which the matrix A = (\begin{pmatrix} -3 & -6 & -18 \ 2 & -9 & -14 \ -8 & 3 & k \end{pmatrix}) has a rank of 2. What is the value of k?
Squared Matrix to get a negative identity matrix?
Title: Can a Squared Matrix Result in a Negative Identity Matrix? Body: Consider the existence of 2 × 2 matrices A such that A² = −I₂. For instance, if A = (\begin{pmatrix} 0 & -1 \ 1 & 0 \end...
consider v={(x,y) :xy=0 } with the usual vector addition and scalar multiplication in R^2 is (v,+,.) a vector space?
Consider the set ( V = {(x, y) \in \mathbb{R}^2 : xy = 0} ) along with the usual vector addition and scalar multiplication defined in ( \mathbb{R}^2 ). Is the pair ( (V, +, \cdot) ) a vector space?
Find a nonzero vector parallel to the line of intersection of the two planes -(3x+3y+z) = -1 and 3x+2y+3z = 2.?
I am looking to find a nonzero vector that is parallel to the line of intersection between the two planes represented by the equations -(3x + 3y + z) = -1 and 3x + 2y + 3z = 2. Could someone assist me...
Can anyone help me with vector spaces?
Let ( F ) be a fixed ( 3 \times 2 ) matrix, and let ( H ) be the set of all ( 2 \times 4 ) matrices ( A ) in ( M ) such that ( FA = 0 ) (where ( 0 ) is the zero matrix in ( N ), a ( 3 \times 4 ) matri...