|1 -2 4 3 1 1 -1 3 Let A be a matrix which is row equivalent to 0 1 1 0 1 0 0 0 -3 Find a basis for the nullspace N(A). Find a basis for the range R(A").

Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: Find a basis for the row space and the rank of the matrix. 20 0 1 (a) a basis for the row space JT…

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Q: X= 3 -2 0 0 -2 1 1 0 +S 1 2 1 Find a Basis for Row B of this Matrix

A: Given:To find: A Basis for Row B of this Matrix.The row space (Row B) of a matrix is the set of all…

Q: 2 Find a basis for the row space of the matrix A = 9. -5 -8 {[ ]} Ex: 42 -8

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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: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: If the matrix of change of basis form the basis B to the basis B'is A= OA °;) 0⁰ (²) -3 2 then the…

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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: (a) Let A, B be n × n symmetric matrices such that XTAX = X™BX for all column vectors X e R". Show…

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Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: 6 Let b₁=[2] b₂ = 3 4 [ C₁ = [ ² ] ² ₂ = 1²²] > V = [] (2 13 2 and C = { C₁₂ (₂} Find and consider…

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Q: |a,6,d e а a, b, d E R}. S2x2 b d Do three matrices 1 A1 = 0 1 1 0 A2 = A3 1 0 - 1 | form a basis of…

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Q: (3) Find an orthogonal basis of the column space of the matrix -1 6 6 3 6 -4 -3, A= 3-8 1-2 1

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Q: Find all Solutions to the matrix equation A·B = B.A wheRe A = [X _Y] and B= x-1 ]

A: You have asked multiple questions. I solve the first question for you. For the remaining part to be…

Q: Use the fact that matrices A and 8 are row-equivalent. 2 10 0 5 11 0 722-2 A = B = 1 2 3 10 23 7 0…

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Q: For what value(s) of k is the matrix A = 1k1 non-invertible (a) All real numbers. (b) All real…

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Q: A symmetric matrix satisfies M= M'. The set of 2 x 2 symmetric matrices S, with standard matrix…

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Q: Part 1: Find the inverse of the matrix A, if it exists. A 033 -4 03 o] 060 06

A: The matrix is: A=033-403060 To Do: We have to find the inverse of the matrix if it exists.   Note-…

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: 2 8. A polynomial p(x) = R²[x] has the coordinate 3 relative to the ordered basis B {1,1+ x,…

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Q: Consider the vector space PA(R) = {ax + bæ³ + ca? + dx + e : a, b, c, d, e E R} of polynomials of…

A: Note:- for this problem you don't mention about f1, f2, f3 (should i have to take  f1, f2, f3…

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: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

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Q: 1 0 -2 1 1 5 0 4 0 8 -1 0 1 0 -2 0 3 3 0 1 1 2 1 1 0 1 4. Let A = and let B 0 0 0 0 0 2 2 0 0 The…

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Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: en the matrix frix.

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Q: Consider the following matrix: 2 -2 4 6 6 A = -1 1 3 2 -3 -1 1-3 -3 1 Give a basis for each of…

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Q: If i had a vector X what was a 2x4 Matrix being |818-2 | | -6 1-6 -2 | How would i find the…

A: let A = 818-2-61-6-2   reduced Echelon form is rref= 100-20110    Equations Form…

Q: | 4B 3B] Consider L 4p ] Find all the values of the parameter ß for which the matrix is invertible.

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Q: Find a basis for the column space of 4 1 3 0 - -31 3 2 1 4 -1 A -3 -2 -1 - -4 2 6 -4 -2 -8 3 Basis…

A: image uploadedExplanation:Step 1: Step 2: Step 3: Step 4:

Q: 8. Let A be the matrix -1 0 1 2 3 2-1 2 4 2 6 65 10, (a) Find a basis for the null space of A (b)…

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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.