69. Collinear Points and Determinants (a) If three points lie on a line, what is the area of the "triangle" that they determine? Use the answer to this question, together with the determinant formula for the area of a triangle, to explain why the points (a, bi), (a2, b.), and (a3, b») are collinear if and only if a, b 1 az bz 1= 0 az b, 1 (b) Use a determinant to check whether each set of points is collinear. Graph them to verify your answer. (i) (-6, 4). (2, 10). (6, 13) (ii) (-5, 10), (2, 6), (15, –2)

Q: 2 18 -3

A: Let's find.

Q: Theorem 4: If at elements in any row (or column) are multiplied by a number, the determinant is also…

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Q: Find the determinant of matrix A by using cofactor expansion. Show your work. 1 A = 0 0 - 1 3 3 -2)…

A: Given matrix A=13-2005131 Now we need to determine the determinant of matrix by cofactor method.

Q: to compare the numbers of operations involved in calculating the determinant of a 10 × 10 matrix by…

A: We use the Row Echelon Form Method.    It is used to reduce the given matrix to triangular form and…

Q: Compute the determinant using a cofactor expansion down the second column. 1 |-2 1 -6 -2 8

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Q: Use the determinant of a matrix to find the area of the triangle whose vertices are (1,7) (0,6) and…

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Q: Let = and %3D Compute the area of the parallelogram determined by four points with position vectors…

A: u→ = 30 v→ = 12 given position vector of parallelogram is u→ , v→, u→+v→, 0→.

Q: Theorem 2: If all elements of any row (or column) are zero except for one element then the value of…

A: Let's Solve,

Q: Theorem 3: An interchange of any two rows (or columns) changes the sign of the determinant GIVE 2…

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Q: (a) Use determinants to compute the area of the parallel- ogram spanned by the vectors (2, 3) and…

A: Note the results : Suppose we have two vectors u=<u1,u2> and v=<v1,v2> .Then area of…

Q: GIVE 2 EXAMPLES FOR THIS THEOREM OF DETERMINANTS Theorem 9: The sum of the products of the elements…

A: To give the examples of the theorem of determinant which is the sum of the products of the elements…

Q: Compute the determinant. What does this imply about the invertibility of the matrix?

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Q: Show how Rule 6 (determinant= 0 if a row is all zero) comes from Rule 3.

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Q: 3. The determinant of an upper triangular n x n matrix or a lower triangular n x n matrix equals the…

A: an upper triangular matrix is those having non-zero elements from the diagonal and above and the…

Q: Compute the determinants using cofactor expansion along any row or column that seems convenient

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Q: (4) Use determinant to find the area of the triangle with vertices (0, 0), (x1,Yı), and (x2, Y2) in…

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Q: Compute determinant of 9 -2 -6 -8 3 6 10 -2 -6

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Q: ind the determinant of the matrix 3 1 -2 5 0 7 -4 -1 4

A: We can find the determinant as below

Q: GIVE 2 EXAMPLES FOR THIS THEOREM OF DETERMINANTS Theorem 6: If we express the elements of each row…

A: We will find out the required examples.

Q: According to determinant properties, when two rows are interchanged then signs of determinant Must…

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Q: Theorem 5: If any two rows (or columns) are the same or proportional, the determinant is zero. GIVE…

A: If any two rows( or columns )are the same or proportional then the determinant is zero.

Q: When finding the determinant using cofactor expansion, it is necessary to select the row or column…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: I'm confused about how we calculate the area of a parallelogram determined by the points (-2,-2),…

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Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A: Co factors of first row: Therefore determinant value is,

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: Given: 252040193

Q: Prove the identity without evaluating the determinant (Using properties). a1 bi + tai ci+rb1 + sa1…

A: We have to prove the identity…

Q: Use Cramer's Rule to solve for x, in the system: -x, - 4x, +x, =-5 3x, +x, - 2x, =-13 2x, – 2x, +x,…

A: Concept:

Q: Take three matrices from your mind and sow if those three satisfy distributive law. Determine the…

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Q: If some row of a square matrix consists only of zeroentries, then the determinant of the matrix…

A: 1. the determinant of a square matrix with a row with all zero entries is zero. By definition the…

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: To find the determinant of the matrix

Q: Use a determinant to find the area of the triangle with th- (-6, 0), (6, 0), (0, 3)

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Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

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Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

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Q: Let u= and v Compute the area of the parallelogram determined by u, v, u-v, and 0, and compute the…

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Q: Use Cramer’s Rule (determinants) to solve the system: [x - y = -5, 3x + 2y = 0].

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Q: Prove that matrix Y is obtained from matrix X. Identify the property of determinants and prove |Y| =…

A: Y=4-984261-25X=1-3-74261-25 Y is obtained from X as shown below.

Q: 1. Can we use cofactor expansion in any n x n matrix? Why? How? 2. Does a 1x 1 matrix has…

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Q: Give three examples of application of determinant in engineering

A: (1) Determinant can be used to find solutions of the multi variable linear equations.

Q: For this question you may use technology to compute such actions as finding determinants, putting a…

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Q: 3279 5 3 6 -5 5-3 -16 9 -6 27 -12 25

A: Given: 3526235-575-3-169-627-12 To prove that the determinants are the same using at 2 rows in Co…

Q: Explain determinants in your own words provide 2 real life/ industerial apllications of determinants

A: Determinant is a factor that directly leads to a decision. In algebra, determinant is the scalar…

Q: for what type of matrix can we evaluate the determinant? what is the determinant?

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Q: Please make it step by step: b.Using Matrix [C] and ‘k’ prove that Property 3 of determinant is…

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Q: ketch the triangle with vertices (3/2, 0), (2, 6), (1, 4) and use a determinate to find its area.

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Q: Compute the area of the parallelogram determined by four points with position vectors ủ, v, ủ + v,…

A: In this question, concept of determinant is applied. Determinant Determinants are a sort of scaling…

Q: The determinant of a certain 3 x 3 matrix (Let's call it Matrix A) is known to be 3. What is the…

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Q: 3 and v = Compute the area of the parallelogram determined by four points with position vectors ū,…

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Q: Compute the determinants using cofactor expansion along any row or column that seems convenient

A: Given 11-12013-21.

Q: 6. 6. - Evaluate the determinant of 3 6- %3D 3

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Q: ombine the methods of row reduction (row of operations) and cofactor expansion to compute the…

A: INTRODUCTION: The determinant can be thought of as a function with a square matrix as its input and…