Consider the bases of R2 B1={(1,0),(1,3)} B2={(0,1),(1,1)} E={(1,0),(0,1)} Correspond M(Id)_B1_E (a base change matrix B1 to E)

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: find the inverse matrix

A: As per the question, we have to form a 3×3 matrix, given the unique symmetrical elements of YBUS(s)…

Q: Find the transpose, A^T, of te matrix.   A =     1 , 2 , 3            a , b , c          4x , 5y…

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Q: (b) B={(-1,3), (2, -1)} and 8' = {(0, 10), (5,0)} (c) B={(2,5), (-1, -3)} and 3' = {e1, e2} (d)…

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Q: Given the matrix below and its corresponding rref(A) and rref(AT) 1000 -2 -| -3 10000 0100 - 12 0 10…

A: Let us find the basis for the null space of A in the next steps.

Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

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Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

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Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

Q: A)  Justify if the matrix A is diagonalizable.B)  Find a matrix T and a diagonal matrix J, such that…

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Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

A: The objective of the question is to prove the identity adj(A)^-1 = (1 / det(A))*A = adj (A^-1) for…

Q: snip

A: The determinant of an orthogonal matrix is always one. Therefore to prove that the given matrix,…

Q: Let -3 4 A-[ 3³ -1], E-[42], F-[^2} = = = -5 Compute the indicated matrix. (If this is not possible,…

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Q: Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices…

A: For the given matrices A, B, and C. We have to choose the correct option.

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: 8. 3 a) Let A = ( 6 1 3 ,B = 6 -2/ %3D 1 Then find the matrix AB. -4 -1

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Q: Number 6 (b and d only!)

A: We have to find the invertible matrix Q

Q: a) Given the matrices A = = i) A-¹. ii) BT if (3AB) = C. = (₁ 2). Find 1 (¹₁3) and C= 3 3 b) If S³R…

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Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

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Q: Given A = 1 1 0 3 Compute 5A *Matrix

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Q: Q1: Find (1) (а)4 + В, (ь) DC, (c) 3A — 2B". (2) Find the inverse of matrix A andD Where : 0 -1 0]…

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Q: : 21 = |-1/v2 1/V2-1 1/V2 1/V2]1 o 01-1/v2 1/V2 31[ 1/V2 1/v2] Given the diagonalized matrix A =…

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Q: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

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Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: image1

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Q: a) Compute the adjugate of the given matrix A and then compute the inverse of the matrix 1 0 2 A = 4…

A: We have to find the adjugate of the matrix A. We know that the adjugate is the synonym of the…

Q: 4 -3 2 Given the matrix A = 5 -2 0 \1/2 3 7 -5/2/ (a) Calculate az31 + a13 and az4 + a24 (b)…

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Q: Find a P'LU factorization of the given matrix A. (Enter each matrix in the form [[row 1], [row…

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Q: then the standard matrix of T is A = 20 17 38 -17 20 T ([²]) = [²9] 17 38 d T ([^]) = [³7], -3 -17…

A: Given: To Find: To determine the standard matrix of transformation T.

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.