determinants interview questions

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Bharani Kumar Depuru is a well known IT personality from Hyderabad. He is the Founder and Director of Innodatatics Pvt Ltd and 360DigiTMG. Bharani Kumar has more than 18 years of experience and has worked for top IT companies like HSBC, ITC Infotech, Infosys, and Deloitte. He has degrees from IIT and ISB. He is a prevalent IT consultant specializing in Industrial Revolution 4. 0 implementation, Data Analytics practice setup, Artificial Intelligence, Big Data Analytics, Industrial IoT, Business Intelligence and Business Management. With more than ten years of experience, Bharani Kumar is also the chief trainer at 360DigiTMG. He has been making it easy for his students to switch to IT. 360DigiTMG is at the forefront of delivering quality education, thereby bridging the gap between academia and industry.

Table of Content

• The characteristic equation of a matrix is: a) det(A – λI) = 1 b) det(A – λI) = 0 c) A = λI d) A = I» The answer is b) det(A – λI) = 0. “An eigen vector is a vector that is represented by a matrix X.” When you multiply matrix A by vector X, the direction of the output matrix stays the same as the direction of vector X. A is any matrix, λ are Eigen values, and X is an Eigen vector. The formula is AX = λX. The equation used to figure out a matrix’s Eigenvalues is known as the matrix’s characteristic equation. Also known as characteristic polynomial. You can write |A – λI| = 0 for any square matrix A and any scalar λ. This equation shows that the matrix (A – λI)X = 0 turns X into the 0 vector. This also means that (A – λI) won’t have an opposite, so its determinant has to be 0. Its property is that det(A – λI) = 0. Its trace is Tr(A), which is equal to the sum of its diagonal elements.
• Which of the following is true about the Cayley-Hamilton theorem in linear algebra? a) Orthogonal Matrix b) Inverse Matrix c) Identity Matrix d) Square Matrix It is true that every square matrix with real or complex numbers meets its characteristic (eigen values) equation. If you turn a square matrix into a polynomial equation (det(A – λI)), you can get the answer 0. As an example, let’s say that A = 1 2 -1 2 and λI = [1 2 [1 0 -1 2] – λ* 0 1] |A – λI| will be a polynomial equation with degree n (since A is a n*n matrix). The polynomial equation λ^2 – 3λ 4 (degree 2, which is the same as the dimension of Matrix A 2*2) is also equal to zero. λ^2 – 3λ + 4 = 0″ .
• Diagonalization of matrix: a) An n*n matrix has n eigenvectors that are linearly independent of each other b) A is similar to a diagonal matrix. c) A = PDP^−1 for a matrix P that can be turned upside down and a diagonal matrix D d) All the Above. Answer – d) All the Above. “the act of taking a square matrix and turning it into a certain kind of diagonal matrix that has the same basic properties as the original matrix” You can also think of diagonalizing as a way to find the eigenvalues of a matrix, which are the diagonal elements of the matrix. ” .
• Which of these is not a square matrix? a) 3×3 matrix b) 2×3 matrix c) 4×3 matrix d) 1×2 matrix i. e. The size of a square matrix is n x n. Since the 1×2 matrix doesn’t have the same number of rows and columns as option D, it is not a square matrix. ” .
• Which of these is not a diagonal matrix? a) [[1,0,0], [0,2,0], [0,0,3]] b) [[1,2,3], [4,5,6], [7,8,9]] c) [[1,0], [0,1], [1,0]] d) [[0,0], [0,0], [0,0]] “A diagonal matrix is a square matrix where all the elements outside the main diagonal are zero.” Therefore, option a) is a diagonal matrix. ” .
• What size is AB if A is a 3×3 matrix and B is a 3×2 matrix? a) 3×2 b) 2×3 c) 3×3 d) 2×2 The answer is a) 3×2. “To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.” A has three rows and three columns, and B has three rows and two columns. This means that AB will have three rows and two columns. ” .
• The determinant of a matrix is a scalar value that can be positive, negative, or zero. It is not a) a scalar value; b) a negative value; c) the sum of its diagonal elements; or d) the product of its eigenvalues. The correct answer is c) the sum of its diagonal elements. If you want to know more about determinants, click here. It’s not the same as the sum of its diagonal parts. On the other hand, the trace of a matrix is the sum of its diagonal points. ” .
• If matrix A’s determinant is zero, what can we say about its inverse? Could it be that it exists and is unique? Could it be that it exists but may not be unique? Could it be that it does not exist? The correct answer is c) It does not exist. This is because you can only find the inverse of a matrix if the determinant is not zero. ” .
• Which of these is not a type of matrix? a) Identity matrix b) Diagonal matrix c) Scalar matrix d) Octagonal matrix The other options are types of matrices. ” .
• a) [[1,2], [3,4]] b) [[2,3,4], [5,6,7], [8,9,10]] c) [[1,2,3], [4,5,6]] d) [[-1,0,1], [2,3,-2], [4,1,1]] The correct answer is c) [[1,2,3], [4,5,6]]: “A square matrix has the same number of rows and columns.” The matrices in choices a), b), and d) are all square, but the matrices in choice c) are not square. ” .
• If A is a 3×4 matrix and B is a 4×2 matrix, what is the size of the product AB? a) 3×2 b) 3×4 c) 4×2 d) 3×3 Answer: a) 3×2 “The product of two matrices A and B is defined only if the number of columns in A is equal to the number of rows in B.” Let A and B each have 4 columns and 4 rows. Then, AB will have 3 columns and 2 rows. ” .
• a) [[1,0], [0,1]] b) [[2,0], [0,2]] c) [[1,2], [3,4]] d) [[0,0], [0,0]] The correct answer is b) [[2,0], [0,2]]. “A scalar matrix is a diagonal matrix where all the diagonal elements are equal.” In choice (b), the matrix is a scalar matrix with diagonal elements that are both 2. ” .
• a) [[1,2], [2,1]] b) [[1,2], [3,4]] c) [[1,0], [0,1]] d) [[0,1], [1,0]] The correct answer is a) [[1,2], [2,1]]: “A matrix is symmetric if it is equal to its transpose.” The matrix in (a) is symmetric because it is the same as its transpose. ” .
• Which of the following is not a type of matrix multiplication? a) Dot product b) Scalar multiplication c) Cross product d) Matrix product? The correct answer is c) Cross product. When you do a cross product, you multiply two vectors together. The other options are all types of matrix multiplication. ” .
• Which of these matrices is not invertible? a) [[1,2], [3,4]] b) [[1,0], [0,1]] c) [[2,4], [1,2]] d) [[1,1], [2,2]] Answer: a) Cross product “A matrix is invertible if its determinant is not equal to zero.” It can’t be turned into a square because its determinant is -2, which is not equal to zero. But the determinant of matrix b) is 1, the determinant of matrix c) is 0, and the determinant of matrix is 0. Therefore, matrices , c), and d) are not invertible. >” .
• a) [[1,2,3]] b) [[1], [2], [3]] c) [[1,2], [3,4]] d) [[1]] The correct answer is a) [[1,2,3]]: “A row matrix is a matrix with only one row.” The matrix in option a) is a row matrix. ” .
• a) [[1,2], [2,1]] b) [[0,1], [-1,0]] c) [[1,0,0], [0,1,0], [0,0,1]] d) [[-1,0], [0,-1]] The correct answer is b) [[0,1], [-1,0]. “A matrix is skew-symmetric if it is equal to the negative of its transpose.” This property is met by the matrix in option b), so it is skew-symmetric. ” .
• Which of the following is not true about the inverse of a matrix? a) The inverse of a matrix is unique b) If a matrix A is invertible, then so is its inverse c) The product of a matrix and its inverse is equal to the identity matrix d) If a matrix A is not invertible, then its inverse can be found by taking the reciprocal of each element This means that choice d) is not a property of the inverse of a matrix. ” .

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FAQ

What is an example of determination in an interview?

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What are the social determinants of Health?

Material Well-Being The Social Gradient. Life expectancy is shorter and most diseases are more common further down the social ladder. Health policy must tackle the social and economic determinants of health. Unemployment. Job security increases health, well-being and job satisfaction.

Do screening questions cover social determinants?

While the screening questions cover most aspects of the determinants, there are areas (transport, earnings, and experiencing exclusion/discrimination) which largely were not covered by the screening instruments. The cross-walk does show a good deal of overlap, however, in how questions are framed to screen for different social determinants.

Why is screening for social determinants of Health important?

Patients’ social needs related to housing, food, safety, etc., can create significant obstacles to high-quality care and contribute to poor health. Screening for social determinants of health without first equipping the practice to address identified needs would be ineffective and unethical.

Are social determinants a business challenge?

From the employer’s perspective, social determinants represent a “profound business challenge,” one felt through increased health plan costs, productivity losses and diminished health equity. And for employees and their families, SDOH are a seemingly insurmountable barrier preventing them from achieving optimal health.