Practice Questions on Matrices

Question 1: Find x so that [Tex]\begin{bmatrix}1 & x & 1\\\end{bmatrix} \begin{bmatrix}1 & 3 & 2\\0 & 5 & 1\\0 & 3 & 2\\\end{bmatrix} \begin{bmatrix}1\\1\\x\\\end{bmatrix} = 0[/Tex]

Question 2: Under what conditions is the matrix equation A²– B² = (A+B).(A+B) true?

Questions 3: Evaluate [Tex]\Delta = \begin{vmatrix}3 & 2 & 1 & 4\\15 & 29 & 2 & 14\\16 & 19 & 3 & 17\\33 & 39 & 8 & 38\end{vmatrix}[/Tex]

Question 4: Evaluate [Tex]\Delta = \begin{vmatrix}a & b & c\\b & c & a\\c & a & b\\\end{vmatrix}[/Tex]

Question 5: Prove that [Tex]\begin{vmatrix}x & a & a & a\\a & x & a & a\\a & a & x & a\\a & a & a & x\\\end{vmatrix} = (x + 3a)(x-a)^3[/Tex]

Question 6: Evaluate [Tex]\Delta = \begin{vmatrix}1 & bc & a(b+c)\\1 & ca & b(c+a)\\1 & ab & c(a+b)\\\end{vmatrix}[/Tex]

Question 7: If a+b+c = 0, then solve the equation [Tex]\begin{vmatrix}a-x & c & b\\c & b-x & a\\b & a & c-x\\\end{vmatrix} = 0[/Tex]

Question 8: Prove that if A is idempotent and A ≠ I, then A is singular.

Question 9: Only a square, non-singular matrix possesses inverse which is unique. State True or False.

Question 10: If AB = 0, does it imply that it is necessary that BA = 0.

Matrices are rectangular arrays of numbers, symbols, or characters where all of these elements are arranged in each row and column. An array is a collection of items arranged at different locations.