True False Linear Algebra
(T) Every invertible matrix is diagonalizable
False
(T) If a matrix A is multiplied by a scalar c, the determinant of the resulting matrix is c*det(A)
False
(T) If det(A) = 2 and det(B) = 3 then det(A+B) = 5
False
A n x n is diagonal if and only if n distinct values
False
Every n x n matrix has distinct e values
False
Every square matrix has real Eigen values
False
Every square matrix is diagonal
False
Every triangular matrix is dragon
False
For any vector in a in R(3), we have ||a x b|| = ||a^2||
False
If A is n x n diagonal matrix there is a unique D that is similar to A
False
If two rows and also two columns of a square matrix A are interchanged, the determinant changes sign
False
If u + v lies in a subspace W of a vector space V, then both u and v are in W
False
If λ is an e-value ... then it's one for A+cI
False
In order for the determinant of a 3 x 3 matrix to be zero, two rows must be parallel
False
Matrix Multiplication is a vector space operation on the set of all square matrices
False
Square matrix is non-singular if and only if it's determined is positive
False
The determinant det(A) is defined for any matrix A
False
The determinant of a 2X2 matrix is a vector
False
The determinant of a 3 x 3 matrix is zero if the points of R(3) given by the rows of the matrix lie in a plane
False
The determinant of a square matrix is the product of all the entries on its main diagonal
False
The formula for A-1 is practical
False
The parallelogram in R(2) determined by non-zero vectors a and b is a square if and only if a dot b = 0
False
The product of a square matrix and it's adjoins is the identity matrix
False
There can be only one e vector Associated with an E value of a linear transformation
False
If A^2 = A, then A = I or 0
False, A = [1,0,1,0]
If AC = BC, then A = B
False, C = 0
Every subset of three non zero vectors in R^2 spans R^2
False, could be dependent set
(T) If V is in a eigenvector of a matrix, then V is a eigenvector of A +cI for all scalars c
True
(T) If an n x n matrix is multiplied by a scalar c, the determinant of the resulting matrix is c^n*det(A)
True
(T) If two rows of a 3 x 3 matrix are interchanged, the sign of the determinant is changed
True
A homogeneous square linear system has a non trivial solution if and only if the determinant of its coefficient matrix is zero
True
A linear transformation having an M x N matrix as a standard matrix representation maps R^n onto R^M
True
Every Subset of four vectors in R^3 is dependent
True
Every elementary Matrix is invertible
True
Every n x n has n e values that may not be distinct
True
Every n x n real symmetrical matrix is real diagonal
True
For every square matrix A, we have det(AA^T) = det(A^tA) = det(A)^2
True
If A = B, then AC = BC
True
If A and B are similar and square, det(A) = det(B)
True
If A and B are similar both are diagonal if the other is
True
If V is a vector space of dimension n, then V is isomorphic to R^n
True
If a square matrix has n real e values it is diagnolizable
True
If det(A) = 2 and det(B) = 3 then det(AB) = 6
True
If the angle between vectors a and b in R(3) IS pi/4 then ||a x b|| = |a dot b|
True
If v is an e-vector if an invertibile matrix A, then cv is an e-vector of A-1
True
The box in R(3) determined by vectors a,b, and c is a cube if and only if all dot products equal zero
True
The column vectors of an n x n matrix are independent if and only if the determinant of the matrix is non zero
True
The determinant det(A) is defined for each square matrix A
True
The determinant of a 3 x 3 matrix is zero if the points in R(3) given by the row of the matrix lie in a plane through the origin
True
The determinant of a 3 x 3 matrix is zero if two rows of the matrix are parallel vectors in R(3)
True
The determinant of a lower triangular square matrix is the product of all entries on its main title
True
The determinant of a square matrix is a scalar
True
The determinant of an elementary matrix is non zero
True
The determinant of an upper triangular square matrix is the product of all entries on its main diagonal
True
The number of independent row vectors in a matrix is the same as the number of independent column vectors
True
The product of a square matrix and it's adjoint matrix is equal to a scalar times the identity matrix
True
The transpose if the adjoint matrix is the matrix of cofactors
True
The vector space P8 is isomorphic to R^9
True
There can be only one e value associated with e vector of a transformation
True
