2000017105 Level: BLet x be a real number. Determine the inverse matrix to the matrix: (cosx−sinxsinxcosx)(cosxsinx−sinxcosx)(1001)(cosxsin2xsinxsin2x−sinxsin2xcosxsin2x)The inverse matrix does not exist.
2000017106 Level: BFor what values of the real parameters a, b, c, d, e and f will the matrices given below be inverse to each other? (100011abc),(def−11−1101)a=−1, b=0, c=1, d=1, e=0, f=0a=1, b=0, c=1, d=−1, e=0, f=1a=−1, b=0, c=−1, d=1, e=0, f=0a=1, b=0, c=−1, d=−1, e=1, f=0
2000017107 Level: BCompute the inverse matrix to the matrix: (17−31427114)(13−42)(134−2)(132−4)(2−341)
2000017108 Level: BFor what values of the real parameters a and b will the matrices given below be inverse to each other? (a731), (−116716b−516)a=5, b=316a=−5, b=316a=5, b=−316a=−5, b=−316
2000017206 Level: BFor what values of a, b and c is the matrix (a−b+c0a−2ba+c−2b2a−2b02b−a0c−a+3b) an identity matrix?a=2, b=1, c=0a=1, b=2, c=1a=2, b=1, c=3a=1, b=1, c=0
2000017208 Level: BLet x∈R. What is the sum of all the entries on the main diagonal of the following matrix? (sin2x015cos2x4sin2x3−1)0124
2000017209 Level: BFor what real value of a is the following matrix an upper triangular matrix? (2a−33+aa−23−a(3)a−11+asin(πa)a−92+3)a=3a=2a=−3a=−2
2000017210 Level: BIn the following matrix, what is the position of the entry with the largest value? (1+2sinπ4tg3π43+cosπ2235+tg(−π)233−4sin2π−2)It lays above the main diagonal.It lays on the main diagonal.It lays under the main diagonal.It lays on the counterdiagonal.
2000017410 Level: BFind the matrix M for which the following equality is true: 3⋅(4−125)−2⋅M=(14−747)(−1214)(1214)(−12−14)(−1−214)
2000017411 Level: BFor which matrix M the following equality holds? 2⋅(5−47−3)−4⋅M=(2−2018−22)(23−14)(2314)(2−3−14)(−23−14)