the determinant of the matrix given below is \[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right]\] A. 2 B. 5 C. 8 D. 16
are 0 and 5 D. cannot be determined" class="read-more button" href="https://exam.pscnotes.com/mcq/the-eigen-values-of-the-matrix-left-beginarray20c-4-2-21-endarray-right-a-are-1-and-4-b-are-1-and-2-c-are-0-and-5-d-cannot-be-determined/#more-20115">Detailed
SolutionThe eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 4&{ – 2} \\ { – 2}&1 \end{array}} \right]\] A. are 1 and 4 B. are -1 and 2 C. are 0 and 5 D. cannot be determined
A unique non-trivial solution exists D. Multiple non-trivial solutions exist" class="read-more button" href="https://exam.pscnotes.com/mcq/for-the-set-of-equations-x1-2x2-x3-4x4-2-3x1-6x2-3x3-12x4-6-the-following-statement-is-true-a-only-the-trivial-solution-x1-x2-x3-x4-0-exists-b-there-are-no-solution-c-a-uni/#more-20116">Detailed SolutionFor the set of equations x1 + 2×2 + x3 + 4×4 = 2 3×1 + 6×2 + 3×3 + 12×4 = 6 the following statement is true: A. Only the trivial solution x1 = x2 = x3 = x4 = 0 exists B. There are no solution C. A unique non-trivial solution exists D. Multiple non-trivial solutions exist
4&7&8 \\ 3&1&5 \\ 9&6&2 \end{array}} \right|\] are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? A. Absolute value remains unchanged but sign will change B. Both absolute value and sign will change C. Absolute value will change but sign will not change D. Both absolute value and sign will remain unchanged" class="read-more button" href="https://exam.pscnotes.com/mcq/if-any-two-columns-of-a-determinant-textp-left-beginarray20c-478-315-962-endarray-right-are-interchanged-which-one-of-the-following-statements-reg/#more-20114">Detailed SolutionIf any two columns of a determinant \[{\text{P}} = \left| {\begin{array}{*{20}{c}} 4&7&8 \\ 3&1&5 \\ 9&6&2 \end{array}} \right|\]
are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? A. Absolute value remains unchanged but sign will change B. Both absolute value and sign will change C. Absolute value will change but sign will not change D. Both absolute value and sign will remain unchanged
5 and 1. What are the eigen values of the matrix S2 = SS? A. 1 and 25 B. 6 and 4 C. 5 and 1 D. 2 and 10" class="read-more button" href="https://exam.pscnotes.com/mcq/eigen-values-of-a-matrix-texts-left-beginarray20c-32-23-endarray-right-are-5-and-1-what-are-the-eigen-values-of-the-matrix-s2-ss-a-1-and-25-b-6-and-4/#more-20113">Detailed SolutionEigen values of a matrix \[{\text{S}} = \left[ {\begin{array}{*{20}{c}} 3&2 \\ 2&3 \end{array}} \right]\] are 5 and 1. What are the eigen values of the matrix S2 = SS? A. 1 and 25 B. 6 and 4 C. 5 and 1 D. 2 and 10
value 3 has a multiplicity of 2, and only one independent eigen vector exists B. Eigen value 3 has a multiplicity of 2, and two independent eigen vector exists C. Eigen value 3 has a multiplicity of 2, and no independent eigen vector exists D. Eigen value are 3 and -3, and two independent eigen vectors exist" class="read-more button" href="https://exam.pscnotes.com/mcq/consider-the-matrix-left-beginarray20c-5-1-41-endarray-right-which-one-of-the-following-statements-is-true-for-the-eigen-values-and-eigen-vectors-of-this-matr/#more-20110">Detailed SolutionConsider the matrix \[\left[ {\begin{array}{*{20}{c}} 5&{ – 1} \\ 4&1 \end{array}} \right]\] . Which one of the following statements is TRUE for the eigen
values and eigen vectors of this matrix? A. Eigen value 3 has a multiplicity of 2, and only one independent eigen vector exists B. Eigen value 3 has a multiplicity of 2, and two independent eigen vector exists C. Eigen value 3 has a multiplicity of 2, and no independent eigen vector exists D. Eigen value are 3 and -3, and two independent eigen vectors exist
statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE? A. S1 implies S2 B. S1 implies S3 C. S2 implies S1 D. S3 implies S2" class="read-more button" href="https://exam.pscnotes.com/mcq/let-m-be-a-real-4-a%c2%97-4-matrix-consider-the-following-statements-s1-m-has-4-linearly-independent-eigenvectors-s2-m-has-4-distinct-eigenvalues-s3-m-is-non-singular-invertible-which-one-am/#more-20111">Detailed SolutionLet M be a real 4 Ã 4 matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE? A. S1 implies S2 B. S1 implies S3 C. S2 implies S1 D. S3 implies S2
are -2 and 6, respectively. What is the other eigen value? A. 5 B. 3 C. 1 D. -1" class="read-more button" href="https://exam.pscnotes.com/mcq/the-minimum-and-the-maximum-eigen-values-of-the-matrix-left-beginarray20c-113-151-311-endarray-right-are-2-and-6-respectively-what-is-the-other-eigen-va/#more-20109">Detailed SolutionThe minimum and the maximum eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 1&1&3 \\ 1&5&1 \\ 3&1&1 \end{array}} \right]\] are -2 and 6, respectively. What is the other eigen value? A. 5 B. 3 C. 1 D. -1
A C. AA’A = $$I$$ D. AA’A = A’" class="read-more button" href="https://exam.pscnotes.com/mcq/a-is-m-a%c2%97-n-full-rank-matrix-with-m-n-and-i-is-an-identity-matrix-let-matrix-a-ata-1at-then-which-one-of-the-following-statement-is-true-a-aa-a-a-b-aa2-a-c-aaa/#more-20108">Detailed SolutionA is m à n full rank matrix with m > n and $$I$$ is an identity matrix. Let matrix A’ = (ATA)-1AT, Then, which one of the following statement is TRUE? A. AA’ A = A B. (AA’)2 = A C. AA’A = $$I$$ D. AA’A = A’