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Linear Algebra
Expand the fuction f(x) = x^4-1 in a series of the formSum of Ak Pk(x)
Linear Algebra
suppose A and B are 3x3 matrices.Show that if B is obtained from A by adding 2 times the first row of A to the last row of A then det(A) = det(B)
Linear Algebra
Find all solutions of this system .
4x + 2y + 3z = 0
3x - y + 2z = 0
x + 2y - z =0
Compare the value of the determinant of the coefficient matrix to zero using the nature of the solution
4x + 2y + 3z = 0
3x - y + 2z = 0
x + 2y - z =0
Compare the value of the determinant of the coefficient matrix to zero using the nature of the solution
Linear Algebra
Suppose C is a 3 x 3 matrix such that det (C) = 4 . Find det (C +C)
Linear Algebra
Let X ∈ Mn×n
, with det X = 0 (i.e. X is not invertible).
Prove or disprove:
There exists an > 0 such that:
Y ∈ Mn×n, kX XY k < =⇒ det Y = 0
, with det X = 0 (i.e. X is not invertible).
Prove or disprove:
There exists an > 0 such that:
Y ∈ Mn×n, kX XY k < =⇒ det Y = 0
Linear Algebra
Suppose A is a 4 * 4 matrix such that det (A) = 16. Find the value of det[4(A^-1)^T ]
Linear Algebra
Show necessary step for the following questions
("For the given matrix"
A=the first row [1 -1] second row [3 2]
B=the first row [3 -2] second row [0 1]
1) show that (A^t)^t=A
2) show that (A+B)^t=A^t+B^t
3) show that (4A)^t=4(A^t)
4) show that (AB)^t=A^tB^t)
("For the given matrix"
A=the first row [1 -1] second row [3 2]
B=the first row [3 -2] second row [0 1]
1) show that (A^t)^t=A
2) show that (A+B)^t=A^t+B^t
3) show that (4A)^t=4(A^t)
4) show that (AB)^t=A^tB^t)
Linear Algebra
(1) Let;
- A=the first row [-1 -1] second row [3 3]. Find all 2×2 materices, B such that AB=0
(2) Distinguish whether the given matrix is symmetric or not
- A=the first row [2 1 3] second row [1 5 -3] third row [3 -3 7]
- B=the first row[1 1 3] second row[1 2 2] third row[3 2 3]
Linear Algebra
Suppose A and B are 3 × 3 matrices. Prove that
(i) (A + B)^T = B^T + A^T
(ii) det (AB)^T = det (A). det (B)
(i) (A + B)^T = B^T + A^T
(ii) det (AB)^T = det (A). det (B)
Linear Algebra
Give the transformation matrix for a shear with direction (3 -4) and factor 4. Apply the transformation to the quadrilateral with vertiees given in counterclockwise order as (2.2),(0 4) ,(-5 1),(3 -2).
