Show that any 3 x 3 matrix of the form a 1 0 1 is defective.

Q: Find the nullspace of the matrix

A:

Q: Construct a 2 x 3 matrix A such that the solution set of the equation Ax = 0 is a line in R3.

A: a)       Result of a system with 2×3 coefficient matrix is a line when system has one free variable.…

Q: Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation [1 0 0 1 АВ - ВА. %3D

A: In this question we have to prove that no 2×2 no matrices the given matrix equation.

Q: Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix…

A: I assume you know what is an argument matrix and what is rank of matrix .

Q: Determine whether the given matrix is diagonalizable 3 1 A = 0 1 3

A:

Q: Explain why the matrix A + C does not exist.

A:

Q: The matrix is not invertible for what value of x 2 1] 3 2 1 1 2

A: The matrix is not invertible the determinant of matrix should be zero.

Q: Show that a nonzero nilpotent matrix is defective.

A:

Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

A: Given matrix is A=2   11   2 and condition is Ax=3x

Q: Is the matrix         1 0 0                               0 1 0                               0 0…

A:

Q: Demonstrate that A A-1 = A-1 A = I

A:

Q: Suppose that A is an m x n matrix and B is an n x m matrix. Then the equation (AB) = ATBT is always…

A: Multiplication Property of transpose : We know that the transpose of a produce of two matrices will…

Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

A:

Q: Find that whether the following matrix is singular or nonsingular. 8 0 -5,

A:

Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

Q: Find a 3 × 1 matrix x with entries not all zero such that

A:

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Is B similar to A?

A:

Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

Q: Show that the matrix is not diagonalizable.

A:

Q: Show that the matrix; is singular

A:

Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: If A is 3 x 3 matrix such that 1 -3 1 1 A 1 -3 Al 1 A 1 1 -3 -2 -4 then A is diagonalizable. Select…

A:

Q: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

A:

Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: If A is 3 x 3 matrix such that (A + I3)² = 0 %3D Show that: A is invertible.

A:

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

A:

Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

A:

Q: Find the value of x so that the matrix is not invertible. 1. 3 2 0 [ 1 2 1 If answer is in decimal,…

A:

Q: Construct a 3 × 2 nonzero matrix A such that: Ax = 0 has only the trivial solution.

A:

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

A:

Q: 2. Let A be a 7 x 5 matrix, and suppose AB is a 7 x 9 matrix for some matrix B. What must the size…

A: We know that matrix multiplication is possible only when number of column of first matrix is equal…

Q: If A is m x n matrix and Ar b has no solution for some b, then %3D

A:

Q: If the first two rows of a matrix A are equal and the matrix product AB is defined, then the first…

A:

Q: Find the dimension of the null space of the given matrix A. 1. -1 4 A = 2 3 -2 1 2 -2

A:

Q: Find the singular values of the given matrix.

A:

Q: Consider the matrix 2 1 A 1 -2 2 1 -2 2 | (a) Is A symmetric? Why or why not? (b) Is A orthogonal?…

A:

Q: If A is what a matrix satis fying A3= A about det A7 %3D can you say

A: We have to find determinants

Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

A:

Q: Find a 3x1 matrix X with entries not all zero such that AX = X , where [1 0 -1] A =1 0 1 4 -4

A:

Q: Find a non-zero 2 × 2 matrix such that -5 -1 0 0 25 ||

A:

Q: Find the LU- Factorization of the matrix A below 1 -2 3 A = 2 1 -4 4 1-4 6. 5 -2

A: Given 21-1-20321-441-465-2

Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

A:

Q: Find c such that the number of the pivots to the matrix below is 2: 1 1 1 -1

A:

Q: Show that the matrix is not diagonalizable.

A: Given matrix The characteristic polynomial of is the only Eigen- values are

Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.