Use a matrix to solve -4x - 4y + 3z = -21-16x - 15y + 13z = 0-8x - 7y + 7z = -12A) 74z, -z, z B) -74z, -z, z C) 74z, -z, 0 D) No solution

Q: 165 -0.31 |-165 -0.173 -0,517 Y EO -165 %3D

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Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: Find a 2 by 2 matrix that reflects the point (x,y) abot the x axis?

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Q: Let A be a 5 × 8 matrix with rank equal to 5 and let b be any vector in R5. Explain why the system…

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Q: Perform the elementary row operation -2R, +R,→R, on the given matrix. 1 2 3 0 -6 -2 Resulting…

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Q: Solve the matrix by using Gauss elimination method x +2z35 3x+4y+2z%3D8 X+3z-10

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Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

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Q: What is the transpose of matrix M=(-1,0,-2)(0,-3,1)?

A: Given -10-20-31

Q: Find the matrix A (in terms of B and C ) if (ЗАТ + 4СТВ)Т3 5A - 4B

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Q: Show that the matrix equation has no solution.

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Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Find a 2x2 matrix that forms an angle of n/3 cadians with the matrix P -- (: 9) 2 0 0 2

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Q: 8, = 3

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Q: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

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Q: Write the augmented matrix corresponding to the system of equations. 3x1  +  2x2      =  0 x1  −…

A: First we will express the given system in Ax= b form and then transform it to augmented matrix form.…

Q: 2 -3 For matrix A = -2A? will be %3D -1 4

A: See the attachment.

Q: Suppose a 5 × 6 matrix A has four pivot columns. What is dim Nul A? Is Col A = ℝ4? Why or why not?

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Q: -4x – y – 6z = -39 -9x + 7y + 4z = 47 – 7x – 6y + z = -52

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Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: The cofactor for the first elemet in the coefficient matrix for this system 2x+3y+3z= 2 4x- 3y-…

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Q: Solve for x, y, z, and win the matrix equation (X, Y, Z, W) wx 2 {]+=[xx]-

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Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

Q: Find the matrix A (in terms of B, C, and D) if (4DA-'B )-1 = C

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Q: Perform the row operation on the given augmented matrix. 1 2 - 1 -3 2 5 1 7 - 2R, + R2 -6 7 Vhat is…

A: Given query is to perform indicated row operation.

Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

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Q: Find the matrix A (in terms of B and C) if (3.4T + 4BC )T= 5.4 – 3C A)}(4B"cT + 3C) (B)}(4C"BI- 3C)…

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Q: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: Suppose M is a (6x6) matrix such that the dimension of its column space is 5 .Then the rank of M is…

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Q: Construct 4x4 matrix A= Lajj whose a entries satisfy Ja;;=2i ij=1, 2, 3,4 %3D

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Q: Let Ax = b be a linear system with real coefficients such that A is an m × n matrix and Ax = b has a…

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Q: Use the row method or column method (as appropriate) to find the first column of BA. -5 3 4 and B =…

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Q: Find 6x6 matrix | a, that satisfies the stated condition. Make your answers as general as possible…

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Q: Suppose that 4x7 matrix collA) = IR* and A hos 4 lead terms. Then NIA) = R %3D %3D O True O False

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Q: Supply a third column so that the matrix will be orthogonal: V5/5 2/3 2/5/5 -1/3 2/3

A: 1. A matrix Q of order n×n is said to be an orthogonal matrix if, QTQ=QQT=In where QTrepresents…

Q: What is the transpose of matrix M=(-1,0,2)(0,-3,1)?

A: A matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.” We…

Q: Solve for C1, C3, C4, C5, & C6 without using matrix. Show the solution. C1-C3=1035.180…

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Q: Supply a third column so that the matrix will be orthogonal: V5/5 2/3 2/5/5 -1/3 0 2/3

A: The given question is related with orthogonal matrix. Given the matrix ,…

Q: Suppose that 4x7 matrix has 4 lead terms. Then collA) = IRt and NIA) = R³ True O False

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Q: Solve these matrix equetions 2 2 3 12 2. 16 -5 4 -6 3 -4

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Q: Let Ax = b be a system of m linear equations in n variables. Designate the columns of A as a1, a2, .…

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Q: :Given : The system in matrix operation form AX=b is| What is the cofactor of 2 in matrix A?

A: WE have to find the cofactor of a(1)(2)=2

Q: how to find the cofactor of a 4x3 matrix

A: Solution

Q: Suppose that a l10 × 8 matrix A has 6 pivot columns. Then dim(ColA)- is Ą and dim(RowA)- is

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Q: 7z + 6y + 5z -2z + 5y 62 3z 4y + hz

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Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: Suppose the above equation is expressed as Ax = b with x = coeffieints of the equations in one…

A: The vector equation is: α21+β13=2025. We need to express it in the form of: A|b and the fill the…

Q: WHe-the syftems of equations as an augmented matrix. 31=- -5x-31+57=-a 7-bx-5y42=- \e

A: to write the augumented matrix we will simply form a 3*3 matrix with co efficients of x,y and z in…

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.