Engineering Mathematics
Linear Algebra
Practice questions from Linear Algebra.
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IncorrectConsider the matrix below:
For which of the following combinations of , and , is the rank of at least three?
(i) and .
(ii) .
(iii) and .
(iv) .
The given matrix is in standard Echelon form,
rank of matrix if or
rank of matrix = 4 if or and
Thus, (i), (iii), (iv) satisfy the echelon form requirement
Consider the vectors
For real-valued scalar variable , the value of
is _________ (rounded off to two decimal places).
denotes the Euclidean norm, i.e., for .
Given:
Let
For
should also minimum.
Let and denote the set of real numbers and the three-dimensional vector space over it, respectively. The value of for which the set of vectors
Dose not form a basis of is__________.
Basis set of vectors is a linearly independent set and hence if the set does not form a basis then the matrix formed by its vectors should have determinant to be 0.
For the set to not form a basis,
Consider the matrix where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
If ,
=0
Similarly, if
Let and be two vectors. The value of the coefficient in the expression , which minimizes the length of the error vector , is
From the given expression, we can write
The error vector can be calculated as.
Taking its magnitude, we get
at
stationary point
Let the sets of eigenvalues and eigenvectors of a matrix be and , respectively. For any invertible matrix , the sets of eigenvalues and eigenvectors of the matrix , where , respectively, are
and
and
and
and
Given input is
are called matrices similar.
Both have same set 7 eigen values
Matrix A & B has different eigen vector.
Let
Eigen vectors of are .
Let be an real column vector with length . The trace of the matrix is
Given the vector length is,
Let
let the Vector in expanding form.
Trace of
