8. (BH) Consider the following matrix: mi1 m12 m13 M = | m21 m22 m23 m21 m22 m23 (a) Show directly that det M = 0. (b) Use your answer to part (a) to show that if a 4 x 4 matrix has two rows the same, its determinant must be zero.

Q: (X1+ 3x2 – 2x3 + X4 = 12 2х1 — х2 + хз + 4x4 3D 2 2х2 — Зхз + 2х4 3x1 Use Cramer's rule to find the…

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Q: Perform one step of row reduction, in order to calculate the values for x and y by back…

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Q: Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient…

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Q: Use determinants to find x, y, and z in t

A: GIven,                 x+y+2z-6=03x+2y+4z-9=02x+3y-6z-3=0

Q: Suppose V₁, V₂ € R³ are nonzero column vectors and V3 = 2v₁ - 32. What is the determinant of the…

A: Given: Suppose  are nonzero column vectors and  We have to find what is the determinant of the…

Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: If the determinant of the 2x2 matrix 3 a 2 b is 7, then what is the determinant of the 2x2 matrix a…

A: To find the determinant of matrix.

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

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Q: Consider the following system 321 + 2z2 + I3 = 3 T1- 2z2 +3zz = 9 221 + 22-2zs =-3 %3D %3D Find the…

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Q: Use the determinant of the coefficient matrix to determine whether the system of linear equations…

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Q: If the determinant of the 2x2 matrix 5   a 8   b is 7, then what is the determinant of the 2x2…

A: TO find the determinant of the matrix  B.