vu mth501 Final Term - Quiz No.4
vu mth501 Linear Algebra Quiz
This quiz belongs to book/course code vu mth501 Linear Algebra of vu organization. We have 4 quizzes available related to the book/course Linear Algebra. This quiz has a total of 7 multiple choice questions (MCQs) to prepare and belongs to topic Final Term. NVAEducation wants its users to help them learn in an easy way. For that purpose, you are free to prepare online MCQs and quizzes.
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Question 2: Let V be a five-dimensional vector space, and let S be a subset of V which spans V. Then S
Must be linearly dependent
Must be a basis for V
Must have infinitely many elements
Must have at most five elements
Question 3: If A be the standard matrix of linear transformation $$T : R^n \rightarrow R^m \(, then which of the following is true for the mapping from \)R^n \( onto \)R^m \( ?
The columns of A span $$ R^n $$.
The columns of A span $$ R^m $$.
The columns of A are linearly independent.
The columns of A are identical.
Question 4: If a system of equations is solved using the Gauss-Seidel method, then which of the following is NOT true about the matrix M that is derived from the coefficient matrix?
All of its entries below the diagonal must be zero.
All of its entries above the diagonal must be zero.
Its determinant is non-zero.
It is an invertible matrix.
Question 5: If \( A =\begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & k & 1 \ end{bmatrix} \), then which of the following is true for the matrix?
det(A) = 1
det(A) = k - 1
det(A) = k
det(A) = k + 1
Question 6: A square matrix A is said to be diagonal if A is similar to a matrix
Column matrix
Zero matrix
Diagonal matrix
None of the given
Question 7: If \(v_1 = (2, 2, 2), v_2 = (0, 0, 3) \) and \(v_3 = (0, 1, 1) \) span \( R^3 \), then which of the following is true for any arbitrary \(b^r = (b_1, b_2, b_3) in R^3 \) ?
\( (0, 1, 1) = k_1 (b_1, b_2, b_3) + k_2 (2, 2, 2) + k_3 (0, 0, 3) \)
\( (b_1, b_2, b_3) = k_1 (2, 2, 2) + k_2 (0, 0, 3) + k_3 (0, 1, 1) \)
\( (0, 0, 3) = k_1 (2, 2, 2) + k_2 (b_1, b_2, b_3) + k_3 (0, 1, 1) \)
\( (0, 1, 1) = k_1 (2, 2, 2) + k_2 (0, 0, 3) + k_3 (b_1, b_2, b_3) \)
