Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple roots a1,..., a6, and suppose that Ja4| = v3. Find (a3 + a4, a6).

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

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

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Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

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

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Find matrices P and D so that A = PDP1 and D is a diagonal

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Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 A= 12 2 -0 12 8 4,

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Q: Let a = (a;) be an n-rowed square matrix and I12 be the matrix obtained by interchanging the first…

A: we have solved this question by using an example.

Q: Which of the following matrices is not in Row Echelon Form (REF)?

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Q: -14] is a linear combination of the vectors 16 if and only if the matrix equation Az = b has a…

A: Solving

Q: Find the charo cteristica poly no nomi the matrix A = 3. 3. /- P(x) = 1.

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Q: Calculate the rank of each matrix by converting it into canonical form…

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Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

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

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Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

Q: 4. Determine whether the matrix is nonsingular or singular. 6ive reasont -11 0 3 2-2 1 le

A: When the determinant of the matrix is zero,                      Then the matrix is said to be…

Q: Find the change of basis matrix from B1 to B2. -1 2

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Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

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Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: Determine the cofactor of 2 in the matrix A = 1 9. 7 4 O-4 3. O -3 2.

A: Cofactor of any element aij is the determinant of the matrix formed by deleting row i and column j…

Q: Show that the matrix; is singular

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Q: Consider the matrix A Calculate A¹00 if = (-5,-4,5). 1 6 2 -1 0

A: Introduction: The power of a matrix is very significant in matrix calculations. It involves the…

Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

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

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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: Enter a 3 x 3 symmetric matrix A that has entries au = 5, az2 = 4, a33 = 0, a12 = 2, a3ı = 1, and…

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Q: Suppose that A, B, C and D are n × n matrices satisfying the equation ABC = D. Show that if DA is…

A: Given:Suppose that A,B,C and D are n×n matrices ABC=DInvertible matrix:A square matix is invertible…

Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: Use the matrix C to find C-1. -5 6 3 2 -2 1 9 7 -12 4 C= 12 2 -7 10 10 3 2 8 7 -4 1 3 9. 23 C-1…

A: Given The given matrix is C=-5632-2197-124122-710103287-4139232

Q: Define the matrices 2, A = 1 ). B- ( ).c-( ). D - ( ) = - (;). 3 4 ‚E 4 3 1 1 2 1 В - C : 2 -4 -2…

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Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

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Q: Find the change-of-coordinates matrix from B to the standard basis in Rr. 8 B=. 4 -8 7 3 7 Pe =0

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Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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Q: Find SVD for the matrix A=[1 2;2 1].

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Q: Find the matrix A given that -1 2 (I2 + 2A)–1 4 5 O a. 1/13 2/13] -5/13 O b. [-1/13 5/13] 2 -1 4/13]…

A: The given equation is:…

Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

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Q: Show that if A is an n × n matrix, then det(AAT ) ≥ 0.

A: Given, A is a n x n matrix. Let AT be the transpose of A. To prove det (AAT) is non-negative.

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

Q: independent

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Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single celI.)…

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

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 6. -4 2 B= 5 -4 7. -3 7…

A: Solution

Q: DHI Reduce each Hhe following matriceg Into Me of indicated form. (i):- -2 3-ノ red uced eehelom fom.…

A: Solve the given problem.

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: Let B and C be bases for R. If B = {(-1, -1), (3, 4)} and the change-of-basis matrix from B to C is…

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Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.