3 13 Given A = - 4 - 12 - 4 observe that the first column plus twice the third column equals the second column, Find a nontrivial solution of Ax = 0 without -3 -15 9- performing row operations. [Hint: Write Ax = 0 as a vector equation.] X =

Q: The vector h = 16 -25 can be written as a linear combination of h 3 -5 -12 and 2 B -3. Find the…

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Q: Perform the indicated operations and express the result in simplest form 3j2-j20+(10+j4)

A: Given expression is 3j2-j20+10+j4.

Q: Write a vector equation that is equivalent to the given system of equations. x₂ + 4x3 = 0 3x1 +6x2x3…

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Q: 8. a.) X + x- 2 X-2

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: If one of the sides of a square is 3x-4y - 12 = 0 and the center is (0, 0), then find the equations…

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Q: If a and 3 are the roots of the quadratic 3r² – 4.x + 6 = 0, find the value of ( + )

A: We have to solve given problem:

Q: Express (-23+ j2) -6 in rectangular form.

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Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: Find all 4 roots of the equation z4+1=0.

A: Concept:

Q: If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the…

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Q: Consider the two vectors A = 5 1 - 3 1 and B = -1-2j. (a) Calculate A + B 51 1+5 (b) Calculate A - B…

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Q: Find the orthogonal Tradectories x2,4ax t4a %3D

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Q: determine the solution set of the linear system: x3-x4=-2 x1-x2+2x4=1 -3x1+3x2+2x3-8x4=-7 write your…

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Q: Detecmine if the Columns of the mahix beom a Tutihy answer linearly independent Set

A: The Matrix given to us is 0-853-74-15-41-32

Q: 4. Convert the equation (x = 10 + 5t : 10 - 2t = to scalar form.

A: Given the problem that the parametric equation is x=10+5ty=10−2tthe aim is to write the equation in…

Q: List five vectors in Span (v₁, V₂}. Do not make a sketch. V1 = 9 4 V2 -6 -4 3 0

A: Consider the provided question,Here, the scaler element are from the field .Therefore, elements of…

Q: Identify the quadric with the given equation and give its equation in standard form   16x2 + 100y2 +…

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Q: Given that write 4 A -4 -5 -2 -57 2 - 3 5 3 61 -3 as a linear combination of the vectors 16 6 5 + [1…

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Q: 1 2. Find the squares of all 3ª roots of 2 2 +

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Q: -18 [] 12 Let u= 40 and A= 2-4 9 Is u in the plane in R³ spanned by the columns of A? Why or why…

A: Given : u=-184012   , A=2-4-5922 To Check : A. u is a linear combination of the Columns of A…

Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

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Q: If the roots of equation x² - 2cx + ab = 0 a the that th of 2 20 41

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Q: Let r₁ and r2 be two different roots of the equation ax² +2bx+c = 0. Without solving the equation,…

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Q: 5a 10a-8

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Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: z² (3+j5)z + j8-5=0

A: We have z2-3+j5z+j8-5=0' The solution of the quadratic equation az2+bz+c=0 is z=-b±b2-4ac2a Now, we…

Q: 15 --0-0-0 , = -8 , and b = 29 -15 Let a₁ = 3 b = 2 a₁+ Is b a linear combination of a₁ and a₂? OA.…

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Q: What are the roots of the equation x2 – 10x + 26 = 0 in simplest a + bi form?

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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.