let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C<0 or A=0 d. c>0 or A=0

Q: Let Q be an orthogonal matrix such that QA makes sense. Show that A and QA have the same singular…

A: Let,

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c) diagonal,…

A:

Q: Let A, B & Mn (C) be Hermitian matrices. Then

A:

Q: Use the Invertible Matrix Theorem to decide if A is invertible

A:

Q: Let A and B be n × n nonsingular matrices. Find nonsingular matrices P and Q so that PAQ = B .

A: Given that the n×n non-singular matrices as A and B. It is known that a matrix is non-singular only…

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: ) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s) for…

A:

Q: State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c) diagonal,…

A: The special kinds of square matrix are: Upper triangular matrix A square matrix is said to be…

Q: Consider an n x n matrix. Give 3 equivalent conditions for A to be invertible

A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: Determine whether th e given matrix is orthogonal. If it is, find its inverse

A: Given: To Find: (a). Whether the matrix is orthogonal. (b). If orthogonal find it's inverse.…

Q: let A nonsingular matrix, c #0, c scalar (cA)" = CA -1 -1 %3D Select one: True O False

A:

Q: Let A be a matrix 4 0 0 0 0 4 0 0 0 0 2 0 1 0 0 2 Determine if A is diagonalizable, and if…

A: Solving the above matrix problem using row operations

Q: Let A be a square matrix. Show that (a) A + A# is Hermitian, (b) A – A# is skew-Hermitian, (c) A =…

A: Explanation of the answer is as follows

Q: Let be the skew operator that transforms a 3x1 column matrix into the 3x3 skew- symmetric matrix…

A: Let us consider  3×1 matrix  n=xyz and we have given [ ]x be the skew symmetric matrix…

Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

A:

Q: Let A be an n xn matrix and B= A+ I, where I is the identity matrix, then it is possible for A and B…

A:

Q: Find the specified change-of-coordinates matrix. Let B= {b1, b2) and C= {c, c2) be bases for R?,…

A:

Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

A:

Q: Find x such that the matrix is singular. A- -2

A:

Q: Find the two by two matrix A such that A -

A:

Q: Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: Find the inserve if it exists, of the following matrix. 1 -1 2 1 1 1 1 2

A:

Q: Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we…

A: The quadratic form is one of the most important parts of linear algebra. Quadratic means degree two.…

Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Find the inserve if it exists, of the following matrix. 1 2 1 1 1 2

A: The give matrix  is, 1 1 -1 2 -1 1 1 1 2 The determinant of the above  matrix is,…

Q: A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E,…

A: A lower triangular matrix of matrix A is  .......

Q: Let A, B, C be invertible matrices of order 3x3. Show that if AB = AC , then B =C. %3D

A: Let A, B, C be invertible matrices of order 3×3. To show that if AB=AC, then B=C.

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

A: Now transpose of this matrix is,

Q: find if the vector x is in the range for matrix A

A:

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

A:

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

A:

Q: Determine whether the matrix A = -1 is diagonalizable. If it is diagonalizable, then find the…

A: The given matrix is  A=010-100002 Finding the eigen values of the given matrix…

Q: Assume A and B are two m × n matrices with the same reduced echelon form. Show that there exists an…

A: Given A and B are two m×n matrices with the same reduced echelon form. We have to show that there…

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A:

Q: Let A be an m xn matrix. Explain why the matrix ATA is symmetric.

A: A square matrix is symmetric if  A^T = A

Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

Q: Q3, Write any matrices A and B of order 3 x 3 and verify the results Let A and B be n x n matrices,…

A: Write any matrices 'A' and 'B' of order 13×3 A=110012003    B=013100100 To verify 1)…

Q: State whether the matrix is diagonalizable or not. [:] 0 7 0 0 O diagonalizable O not diagonalizable

A: Given matrix is 0700 and now subtract λ from the diagonal elements=0-λ700-λThe determinant is…

Q: Q3, Write any matrices A and B of order 3 × 3 and verify the results Let A and B be n n matrices,…

A:

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

A: Given: A=1011

Q: Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P =…

A: First we need to find eigen values:

Q: Gve an example of a dx2 matrix A and 2-dimensional vectors u and v such that u and v are orthogonal…

A: We have to give an example of a 2×2 matrix.

Q: Let Q be an orthogonal matrix such that QA makes sense.                          Show that (QA)+ =…

A: Given, A be a matrix and Q be an orthogonal matrix such that QA makes sense. We have to use product…

Q: Let A be a mxn matrix that n > m (a) Explain why A = 0 has at least a non-trivial solution. %3D

A: (a) Given that A is an m×n matrix. The objective is to explain why Ax=0has non trivial solution.…

Q: Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.