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Chapter 1: Q13E (page 39)

If A is a non-zero matrix of the form [a-bba],then the rank of A must be 2.

Short Answer

Expert verified

True, If A is a non-zero matrix of the form, a-bbathen the rank of A is 2.

Step by step solution

01

Step 1:Rank of a matrix

For the matrix, if we need to find the rank of the matrix, we will find the determinant of a matrix.

We have.A=a-bba鈬�A=a2+b2

02

Justification of answer  

Now, since the value of a and b can鈥檛 be zero at the same time. Because A is a non-zero matrix.

鈬�a2+b2鈮�0

Thus, the rank of the matrix will be 2.

Hence, it is true thatIf A is a non-zero matrix of the formrole="math" localid="1659642906283" a-bba,then the rank of A is 2.

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|4x1+3x2-2x3-x4=45x1+4x2-3x3-x4=4-2x1-2x2-x3-2x4=-311x1+6x2+4x3-x4=11|
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