# MTH 105 TMA Questions & Answers

`Question:  is the science of numbers and shapeAnswer:A: Mathematics Question: is the science of reasoning or explaining eventsAnswer:A: Logic  Question: is the study and analysis of a mathematical proposition as to ascertain the  Truth  Value of the propositionAnswer:A: Logic  Question: Given that 2  3  4 the Truth Value of this statement is Answer:A: false Question: Lagos is a cosmopolitan state The Truth Value of this isAnswer:A: trueQuestion:  is used to analyze the Truth Value of any mathematical statementAnswer:A: Truth Value Table   Question: A statement or proposition in the context of logic is Answer:A: a declarative sentences or an expression of words which are either true or false  but  cannot assume bothQuestion: The connective Rightarrow in logic is a Answer:A: conditionalQuestion: The connective  Lightrightarrow in logic is a Answer:A: bi  implication    Question:  is said to be formed when the conjunction of a set of simple mathematical  statements gives rise to another mathematical statementAnswer:A: An argumentQuestion: What is the common difference in the sequence 3 5 7 9 11Answer:A: 2Question: Evaluate fracz1  3  2i z2  4  3iAnswer:A: 359Question: What is the distance between the points z1 and z2 given that z1  3  2i  and  z2  4  3iAnswer:A: 2Question: Find the unit vectors in the direction of the vector  a4i3jAnswer:A: 5Question: Given that  r1  3i  5 j  r2  4i 19 j Find the modulus of 5r1  r2Answer:A: 1992Question: What is the magnitude of the vectors  3i  4 jAnswer:A: 5Question: If P  T  P and P  F  F implies Answer:A: Identity Laws  Question: If p  q  q p and  p  q  q p implies anAnswer:A: Commutative Laws    Question:  is the use of connectives to combine two or more simple statements to form just one Answer:A: composite statement    Question: The connective wedge in logic is a Answer:A: conjunctionQuestion: Given that x  2y  3 3x  4y 1 What is x and yAnswer:A:  5  4     Question: Which of the following statements is true Answer:A: pvee qwedge pvee rpveeqwedge rQuestion: A necessary and sufficient condition for a matrix square A to be  invertible is  thatAnswer:A: Aneq 0Question: A matrix in which all its diagonal elements are one 1 where all other   elements are zero is calledAnswer:A: identity matrix    `

```Question: The of a matrix is the inter  changing of its row with the columnAnswer:A: transpose matrix     Question: Let Abeginpmatrix123450214endpmatrix then the cofactor of matrix A is the matrixAnswer:A: beginpmatrix20 16 16 5  23 1512 3endpmatrixQuestion: Calculate the determinant of the matrix Abeginpmatrix1234 50214endpmatrixAnswer:A:  10Question: Given that Abeginpmatrix123456endpmatrix and Bbeginpmatrix123  456endpmatrix What is ABAnswer:A: ABbeginpmatrix22284964endpmatrixQuestion: What is the determinant of the Abeginpmatrix 12 3 4 endpmatrixAnswer:A:  2Question:  reads the goods are standard if and only if the goods are expensiveAnswer:pleftrightarrow qQuestion: A matrix that has elements only on its diagonal is calledAnswer:diagonal matrixQuestion: pwedge q qvee p  and pvee q  qvee p implies an Answer:Commutative LawsQuestion: pvee qvee rpvee qvee r  and pwedge qwedge r  pwedge qwedge r implies an Answer:Associative lawsQuestion: given thatAeginpmatrix1  2  3 4  5  6 endpmatrixand Beginpmatrix 1  2 3 4 5 6 endpmatrix Find ABAnswer:eginpmatrix 5  12  15 19  26  31 29  40  51 endpmatrixQuestion: A matrix in which its transpose is equal to itself is calledAnswer:symmetric matrixQuestion: is equivalent to pvee qAnswer:pleftrightarrow qQuestion: which of the following statement is trueAnswer:pvee qwedge pvee rpvee qwedge rQuestion: is a rectangular array of numbers with reference to specific rules governing the arrayAnswer:MatrixQuestion: given thatAbeginpmatrix1  2  3 4  5  6 endpmatrixrnand Bbeginpmatrix 1  2 3 4 5 6 endpmatrixrn Find ABAnswer:D: beginpmatrix 5  12  15 19  26  31 29  40  51 endpmatrixQuestion: Given that x  2y  3z 1 3x  2y  z  4 x  3y  2z  0 What is xy and zAnswer:74 3414Question: What is the common difference in the sequence 3 5 7 9 11cdotsAnswer:2Question: Given that Aeginpmatrix 2  0  1 k  2  3 2  1  4 endpmatrix what is the value of k if A is said to be a singular matrixAnswer: 6Question: Given that Aeginpmatrix 1  2  3 3  2  1 1  3  2 endpmatrix Find the determinant of AAnswer:3Question: let Aeginpmatrix 1  2  3 4  5  0 2  1  4 endpmatrix then the cofactor of matrix A is the matrixAnswer:Aeginpmatrix 20   16   6  5   2  3  15  12   3 endpmatrixQuestion: A matrix is said to be singular if the determinant is equal toAnswer:zeroQuestion: Given that eginpmatrix 1  3 k  4 endpmatrix is singular matrix Find the value of kAnswer:43Question: A necessary and sufficient condition for a matrix square A to be  invertible is thatAnswer:A is not equal zeroQuestion: Calculate the determinant of the matrix Aeginpmatrix 1  2  3 4  5  0 2  1  4 endpmatrixAnswer: 10Question: Given that beginpmatrix 1  3 k  4 endpmatrix is singular matrix Find the value of kAnswer:43Question: Given that Abeginpmatrix 1  2  3 3  2  1 1  3  2 endpmatrix Find the determinant of AAnswer:3Question: Given that Abeginpmatrix 2  0  1 k  2  3 2  1  4 endpmatrix what is the value of k if A is said to be a singular matrixAnswer: 6Question: let Abeginpmatrix 1  2  3 4  5  0 2  1  4 endpmatrix then the cofactor of matrix A is the matrixAnswer:Abeginpmatrix 20   16   6  5   2  3  15  12   3 endpmatrixQuestion: Calculate the determinant of the matrix Abeginpmatrix 1  2  3 4  5  0 2  1  4 endpmatrixAnswer: 10

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